The course aims to provide an introduction to basic concepts of discrete mathematics and linear algebra useful in science and engineering. The various topics will be approached using a concrete approach, using examples and problems to motivate the subject and to help student participation.
Curriculum
Canali
scheda docente
materiale didattico
Matrices and operations between matrices. Linear systems and their resolution.
Matematica discreta e applicazioni
Zanichelli 2008
Programma
Matrices and operations between matrices. Linear systems and their resolution.
Testi Adottati
Giulia Maria Piacentini CattaneoMatematica discreta e applicazioni
Zanichelli 2008
Bibliografia Di Riferimento
Nicholson Algebra lineare McGraw-Hill 2001Modalità Frequenza
recommended attendanceModalità Valutazione
written test
scheda docente
materiale didattico
Vectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Lines and Planes through the origin. Midpoint.
2. Linear combinations of vectors
Linear dependence and independence of vectors.
3. Vector spaces
Definitions, examples and properties.
4. Linear subspaces
5. How to generate linear subspaces
Linear combination and generators.
6. Linear dependence and independence
7. Basis of a linear subspace
Basis. Dimensions. Solution set of a homogeneous system and its dimensions.
8. Vector subspaces sum and intersection
Definitions and examples. Grassmann formula.
9. Affine space
Lines in planes and space. Planes in space. Affine subspace.
10. Homomorphisms
Homomorphism between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
11. Image of a matrix
Properties of a homomorphism image and how to compute it. Surjective homomorphism.
12. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.
13. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.
14. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.
15. Diagonalizing a matrix
Rules and examples.
"Geometria"
Programma
1. Geometric vectorsVectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Lines and Planes through the origin. Midpoint.
2. Linear combinations of vectors
Linear dependence and independence of vectors.
3. Vector spaces
Definitions, examples and properties.
4. Linear subspaces
5. How to generate linear subspaces
Linear combination and generators.
6. Linear dependence and independence
7. Basis of a linear subspace
Basis. Dimensions. Solution set of a homogeneous system and its dimensions.
8. Vector subspaces sum and intersection
Definitions and examples. Grassmann formula.
9. Affine space
Lines in planes and space. Planes in space. Affine subspace.
10. Homomorphisms
Homomorphism between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
11. Image of a matrix
Properties of a homomorphism image and how to compute it. Surjective homomorphism.
12. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.
13. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.
14. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.
15. Diagonalizing a matrix
Rules and examples.
Testi Adottati
G. Accascina e V. Monti,"Geometria"
Bibliografia Di Riferimento
G. Accascina e V. Monti, "Geometria"Modalità Frequenza
Attendance is not mandatory but is strongly recommended.Modalità Valutazione
The final examination is a written test, consisting of both exercises and theoretical questions. The course also includes mid-term assessments at the end of each module. An integrative oral examination may be taken at the discretion of the lecturer.
scheda docente
materiale didattico
Vectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Lines and Planes through the origin. Midpoint.
2. Linear combinations of vectors
Linear dependence and independence of vectors.
3. Vector spaces
Definitions, examples and properties.
4. Linear subspaces
5. How to generate linear subspaces
Linear combination and generators.
6. Linear dependence and independence
7. Basis of a linear subspace
Basis. Dimensions. Solution set of a homogeneous system and its dimensions.
8. Vector subspaces sum and intersection
Definitions and examples. Grassmann formula.
9. Affine space
Lines in planes and space. Planes in space. Affine subspace.
10. Homomorphisms
Homomorphism between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
11. Image of a matrix
Properties of a homomorphism image and how to compute it. Surjective homomorphism.
12. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.
13. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.
14. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.
15. Diagonalizing a matrix
Rules and examples.
"Geometria"
Programma
1. Geometric vectorsVectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Lines and Planes through the origin. Midpoint.
2. Linear combinations of vectors
Linear dependence and independence of vectors.
3. Vector spaces
Definitions, examples and properties.
4. Linear subspaces
5. How to generate linear subspaces
Linear combination and generators.
6. Linear dependence and independence
7. Basis of a linear subspace
Basis. Dimensions. Solution set of a homogeneous system and its dimensions.
8. Vector subspaces sum and intersection
Definitions and examples. Grassmann formula.
9. Affine space
Lines in planes and space. Planes in space. Affine subspace.
10. Homomorphisms
Homomorphism between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
11. Image of a matrix
Properties of a homomorphism image and how to compute it. Surjective homomorphism.
12. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.
13. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.
14. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.
15. Diagonalizing a matrix
Rules and examples.
Testi Adottati
G. Accascina e V. Monti,"Geometria"
Bibliografia Di Riferimento
G. Accascina e V. Monti, "Geometria"Modalità Frequenza
Attendance is not mandatory but is strongly recommended.Modalità Valutazione
The final examination is a written test, consisting of both exercises and theoretical questions. The course also includes mid-term assessments at the end of each module. An integrative oral examination may be taken at the discretion of the lecturer.Canali
scheda docente
materiale didattico
Matrices and operations between matrices. Linear systems and their resolution.
Matematica discreta e applicazioni
Zanichelli 2008
Programma
Matrices and operations between matrices. Linear systems and their resolution.
Testi Adottati
Giulia Maria Piacentini CattaneoMatematica discreta e applicazioni
Zanichelli 2008
Bibliografia Di Riferimento
Nicholson Algebra lineare McGraw-Hill 2001Modalità Frequenza
recommended attendanceModalità Valutazione
written test
scheda docente
materiale didattico
Vectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Lines and Planes through the origin. Midpoint.
2. Linear combinations of vectors
Linear dependence and independence of vectors.
3. Vector spaces
Definitions, examples and properties.
4. Linear subspaces
5. How to generate linear subspaces
Linear combination and generators.
6. Linear dependence and independence
7. Basis of a linear subspace
Basis. Dimensions. Solution set of a homogeneous system and its dimensions.
8. Vector subspaces sum and intersection
Definitions and examples. Grassmann formula.
9. Affine space
Lines in planes and space. Planes in space. Affine subspace.
10. Homomorphisms
Homomorphism between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
11. Image of a matrix
Properties of a homomorphism image and how to compute it. Surjective homomorphism.
12. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.
13. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.
14. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.
15. Diagonalizing a matrix
Rules and examples.
"Geometria"
Programma
1. Geometric vectorsVectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Lines and Planes through the origin. Midpoint.
2. Linear combinations of vectors
Linear dependence and independence of vectors.
3. Vector spaces
Definitions, examples and properties.
4. Linear subspaces
5. How to generate linear subspaces
Linear combination and generators.
6. Linear dependence and independence
7. Basis of a linear subspace
Basis. Dimensions. Solution set of a homogeneous system and its dimensions.
8. Vector subspaces sum and intersection
Definitions and examples. Grassmann formula.
9. Affine space
Lines in planes and space. Planes in space. Affine subspace.
10. Homomorphisms
Homomorphism between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
11. Image of a matrix
Properties of a homomorphism image and how to compute it. Surjective homomorphism.
12. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.
13. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.
14. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.
15. Diagonalizing a matrix
Rules and examples.
Testi Adottati
G. Accascina e V. Monti,"Geometria"
Bibliografia Di Riferimento
G. Accascina e V. Monti, "Geometria"Modalità Frequenza
Attendance is not mandatory but is strongly recommended.Modalità Valutazione
The final examination is a written test, consisting of both exercises and theoretical questions. The course also includes mid-term assessments at the end of each module. An integrative oral examination may be taken at the discretion of the lecturer.
scheda docente
materiale didattico
Vectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Lines and Planes through the origin. Midpoint.
2. Linear combinations of vectors
Linear dependence and independence of vectors.
3. Vector spaces
Definitions, examples and properties.
4. Linear subspaces
5. How to generate linear subspaces
Linear combination and generators.
6. Linear dependence and independence
7. Basis of a linear subspace
Basis. Dimensions. Solution set of a homogeneous system and its dimensions.
8. Vector subspaces sum and intersection
Definitions and examples. Grassmann formula.
9. Affine space
Lines in planes and space. Planes in space. Affine subspace.
10. Homomorphisms
Homomorphism between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
11. Image of a matrix
Properties of a homomorphism image and how to compute it. Surjective homomorphism.
12. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.
13. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.
14. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.
15. Diagonalizing a matrix
Rules and examples.
"Geometria"
Programma
1. Geometric vectorsVectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Lines and Planes through the origin. Midpoint.
2. Linear combinations of vectors
Linear dependence and independence of vectors.
3. Vector spaces
Definitions, examples and properties.
4. Linear subspaces
5. How to generate linear subspaces
Linear combination and generators.
6. Linear dependence and independence
7. Basis of a linear subspace
Basis. Dimensions. Solution set of a homogeneous system and its dimensions.
8. Vector subspaces sum and intersection
Definitions and examples. Grassmann formula.
9. Affine space
Lines in planes and space. Planes in space. Affine subspace.
10. Homomorphisms
Homomorphism between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
11. Image of a matrix
Properties of a homomorphism image and how to compute it. Surjective homomorphism.
12. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.
13. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.
14. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.
15. Diagonalizing a matrix
Rules and examples.
Testi Adottati
G. Accascina e V. Monti,"Geometria"
Bibliografia Di Riferimento
G. Accascina e V. Monti, "Geometria"Modalità Frequenza
Attendance is not mandatory but is strongly recommended.Modalità Valutazione
The final examination is a written test, consisting of both exercises and theoretical questions. The course also includes mid-term assessments at the end of each module. An integrative oral examination may be taken at the discretion of the lecturer.Canali
scheda docente
materiale didattico
Matrices and operations between matrices. Linear systems and their resolution.
Matematica discreta e applicazioni
Zanichelli 2008
Programma
Matrices and operations between matrices. Linear systems and their resolution.
Testi Adottati
Giulia Maria Piacentini CattaneoMatematica discreta e applicazioni
Zanichelli 2008
Bibliografia Di Riferimento
Nicholson Algebra lineare McGraw-Hill 2001Modalità Frequenza
recommended attendanceModalità Valutazione
written test
scheda docente
materiale didattico
Vectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Lines and Planes through the origin. Midpoint.
2. Linear combinations of vectors
Linear dependence and independence of vectors.
3. Vector spaces
Definitions, examples and properties.
4. Linear subspaces
5. How to generate linear subspaces
Linear combination and generators.
6. Linear dependence and independence
7. Basis of a linear subspace
Basis. Dimensions. Solution set of a homogeneous system and its dimensions.
8. Vector subspaces sum and intersection
Definitions and examples. Grassmann formula.
9. Affine space
Lines in planes and space. Planes in space. Affine subspace.
10. Homomorphisms
Homomorphism between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
11. Image of a matrix
Properties of a homomorphism image and how to compute it. Surjective homomorphism.
12. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.
13. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.
14. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.
15. Diagonalizing a matrix
Rules and examples.
"Geometria"
Programma
1. Geometric vectorsVectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Lines and Planes through the origin. Midpoint.
2. Linear combinations of vectors
Linear dependence and independence of vectors.
3. Vector spaces
Definitions, examples and properties.
4. Linear subspaces
5. How to generate linear subspaces
Linear combination and generators.
6. Linear dependence and independence
7. Basis of a linear subspace
Basis. Dimensions. Solution set of a homogeneous system and its dimensions.
8. Vector subspaces sum and intersection
Definitions and examples. Grassmann formula.
9. Affine space
Lines in planes and space. Planes in space. Affine subspace.
10. Homomorphisms
Homomorphism between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
11. Image of a matrix
Properties of a homomorphism image and how to compute it. Surjective homomorphism.
12. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.
13. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.
14. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.
15. Diagonalizing a matrix
Rules and examples.
Testi Adottati
G. Accascina e V. Monti,"Geometria"
Bibliografia Di Riferimento
G. Accascina e V. Monti, "Geometria"Modalità Frequenza
Attendance is not mandatory but is strongly recommended.Modalità Valutazione
The final examination is a written test, consisting of both exercises and theoretical questions. The course also includes mid-term assessments at the end of each module. An integrative oral examination may be taken at the discretion of the lecturer.
scheda docente
materiale didattico
Vectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Lines and Planes through the origin. Midpoint.
2. Linear combinations of vectors
Linear dependence and independence of vectors.
3. Vector spaces
Definitions, examples and properties.
4. Linear subspaces
5. How to generate linear subspaces
Linear combination and generators.
6. Linear dependence and independence
7. Basis of a linear subspace
Basis. Dimensions. Solution set of a homogeneous system and its dimensions.
8. Vector subspaces sum and intersection
Definitions and examples. Grassmann formula.
9. Affine space
Lines in planes and space. Planes in space. Affine subspace.
10. Homomorphisms
Homomorphism between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
11. Image of a matrix
Properties of a homomorphism image and how to compute it. Surjective homomorphism.
12. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.
13. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.
14. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.
15. Diagonalizing a matrix
Rules and examples.
"Geometria"
Programma
1. Geometric vectorsVectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Lines and Planes through the origin. Midpoint.
2. Linear combinations of vectors
Linear dependence and independence of vectors.
3. Vector spaces
Definitions, examples and properties.
4. Linear subspaces
5. How to generate linear subspaces
Linear combination and generators.
6. Linear dependence and independence
7. Basis of a linear subspace
Basis. Dimensions. Solution set of a homogeneous system and its dimensions.
8. Vector subspaces sum and intersection
Definitions and examples. Grassmann formula.
9. Affine space
Lines in planes and space. Planes in space. Affine subspace.
10. Homomorphisms
Homomorphism between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
11. Image of a matrix
Properties of a homomorphism image and how to compute it. Surjective homomorphism.
12. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.
13. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.
14. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.
15. Diagonalizing a matrix
Rules and examples.
Testi Adottati
G. Accascina e V. Monti,"Geometria"
Bibliografia Di Riferimento
G. Accascina e V. Monti, "Geometria"Modalità Frequenza
Attendance is not mandatory but is strongly recommended.Modalità Valutazione
The final examination is a written test, consisting of both exercises and theoretical questions. The course also includes mid-term assessments at the end of each module. An integrative oral examination may be taken at the discretion of the lecturer.Canali
scheda docente
materiale didattico
Matrices and operations between matrices. Linear systems and their resolution.
Matematica discreta e applicazioni
Zanichelli 2008
Programma
Matrices and operations between matrices. Linear systems and their resolution.
Testi Adottati
Giulia Maria Piacentini CattaneoMatematica discreta e applicazioni
Zanichelli 2008
Bibliografia Di Riferimento
Nicholson Algebra lineare McGraw-Hill 2001Modalità Frequenza
recommended attendanceModalità Valutazione
written test
scheda docente
materiale didattico
Vectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Lines and Planes through the origin. Midpoint.
2. Linear combinations of vectors
Linear dependence and independence of vectors.
3. Vector spaces
Definitions, examples and properties.
4. Linear subspaces
5. How to generate linear subspaces
Linear combination and generators.
6. Linear dependence and independence
7. Basis of a linear subspace
Basis. Dimensions. Solution set of a homogeneous system and its dimensions.
8. Vector subspaces sum and intersection
Definitions and examples. Grassmann formula.
9. Affine space
Lines in planes and space. Planes in space. Affine subspace.
10. Homomorphisms
Homomorphism between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
11. Image of a matrix
Properties of a homomorphism image and how to compute it. Surjective homomorphism.
12. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.
13. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.
14. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.
15. Diagonalizing a matrix
Rules and examples.
"Geometria"
Programma
1. Geometric vectorsVectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Lines and Planes through the origin. Midpoint.
2. Linear combinations of vectors
Linear dependence and independence of vectors.
3. Vector spaces
Definitions, examples and properties.
4. Linear subspaces
5. How to generate linear subspaces
Linear combination and generators.
6. Linear dependence and independence
7. Basis of a linear subspace
Basis. Dimensions. Solution set of a homogeneous system and its dimensions.
8. Vector subspaces sum and intersection
Definitions and examples. Grassmann formula.
9. Affine space
Lines in planes and space. Planes in space. Affine subspace.
10. Homomorphisms
Homomorphism between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
11. Image of a matrix
Properties of a homomorphism image and how to compute it. Surjective homomorphism.
12. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.
13. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.
14. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.
15. Diagonalizing a matrix
Rules and examples.
Testi Adottati
G. Accascina e V. Monti,"Geometria"
Bibliografia Di Riferimento
G. Accascina e V. Monti, "Geometria"Modalità Frequenza
Attendance is not mandatory but is strongly recommended.Modalità Valutazione
The final examination is a written test, consisting of both exercises and theoretical questions. The course also includes mid-term assessments at the end of each module. An integrative oral examination may be taken at the discretion of the lecturer.
scheda docente
materiale didattico
Vectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Lines and Planes through the origin. Midpoint.
2. Linear combinations of vectors
Linear dependence and independence of vectors.
3. Vector spaces
Definitions, examples and properties.
4. Linear subspaces
5. How to generate linear subspaces
Linear combination and generators.
6. Linear dependence and independence
7. Basis of a linear subspace
Basis. Dimensions. Solution set of a homogeneous system and its dimensions.
8. Vector subspaces sum and intersection
Definitions and examples. Grassmann formula.
9. Affine space
Lines in planes and space. Planes in space. Affine subspace.
10. Homomorphisms
Homomorphism between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
11. Image of a matrix
Properties of a homomorphism image and how to compute it. Surjective homomorphism.
12. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.
13. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.
14. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.
15. Diagonalizing a matrix
Rules and examples.
"Geometria"
Programma
1. Geometric vectorsVectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Lines and Planes through the origin. Midpoint.
2. Linear combinations of vectors
Linear dependence and independence of vectors.
3. Vector spaces
Definitions, examples and properties.
4. Linear subspaces
5. How to generate linear subspaces
Linear combination and generators.
6. Linear dependence and independence
7. Basis of a linear subspace
Basis. Dimensions. Solution set of a homogeneous system and its dimensions.
8. Vector subspaces sum and intersection
Definitions and examples. Grassmann formula.
9. Affine space
Lines in planes and space. Planes in space. Affine subspace.
10. Homomorphisms
Homomorphism between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
11. Image of a matrix
Properties of a homomorphism image and how to compute it. Surjective homomorphism.
12. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.
13. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.
14. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.
15. Diagonalizing a matrix
Rules and examples.
Testi Adottati
G. Accascina e V. Monti,"Geometria"
Bibliografia Di Riferimento
G. Accascina e V. Monti, "Geometria"Modalità Frequenza
Attendance is not mandatory but is strongly recommended.Modalità Valutazione
The final examination is a written test, consisting of both exercises and theoretical questions. The course also includes mid-term assessments at the end of each module. An integrative oral examination may be taken at the discretion of the lecturer.