The aim of the course is to show both the theoretical and the practical side of the basics in linear algebra and geometry. This will allow the student to obtain a flexible foundation well suited for describing, interpreting and solving problems connected with biomedical engineering
Curriculum
Canali
teacher profile teaching materials
Tentative Course Schedule
Sets and Functions: numerical sets, Cartesian product, domain, codomain, graphs, and properties (injective, surjective, invertible).
Linear Systems: definition, geometric interpretation, solution methods, Gauss elimination algorithm.
Matrices: operations, row echelon forms, rank, invertible and symmetric matrices, determinant and its properties.
Vector Spaces: definitions, examples, subspaces, sum, and intersection.
Systems of Vectors: linear dependence, independence, span, bases, and dimension.
Changes of Basis and Coordinates: Grassmann's formula and direct sum.
Linear Maps (Linear Transformations): kernel, image, composition, isomorphisms, matrix representation.
Endomorphisms: eigenvalues, eigenvectors, characteristic polynomial, diagonalization.
Inner Products: orthogonal bases, norm, spectral theorem, diagonalization of symmetric matrices.
Practical Exercises and Applications on the covered topics.
Programme
SyllabusTentative Course Schedule
Sets and Functions: numerical sets, Cartesian product, domain, codomain, graphs, and properties (injective, surjective, invertible).
Linear Systems: definition, geometric interpretation, solution methods, Gauss elimination algorithm.
Matrices: operations, row echelon forms, rank, invertible and symmetric matrices, determinant and its properties.
Vector Spaces: definitions, examples, subspaces, sum, and intersection.
Systems of Vectors: linear dependence, independence, span, bases, and dimension.
Changes of Basis and Coordinates: Grassmann's formula and direct sum.
Linear Maps (Linear Transformations): kernel, image, composition, isomorphisms, matrix representation.
Endomorphisms: eigenvalues, eigenvectors, characteristic polynomial, diagonalization.
Inner Products: orthogonal bases, norm, spectral theorem, diagonalization of symmetric matrices.
Practical Exercises and Applications on the covered topics.
Core Documentation
Abate-de Fabritiis, Geometria analitica con elementi di algebra lineare, ed. McGraw-Hill, IV edizione. Lecture notes.Reference Bibliography
Abate-de Fabritiis, Geometria analitica con elementi di algebra lineare, ed. McGraw-Hill.Type of evaluation
Written and oral examination. The possibility of holding intermediate exams (midterms) that may exempt students from the written exam will be evaluated.Canali
teacher profile teaching materials
Tentative Course Schedule
Sets and Functions: numerical sets, Cartesian product, domain, codomain, graphs, and properties (injective, surjective, invertible).
Linear Systems: definition, geometric interpretation, solution methods, Gauss elimination algorithm.
Matrices: operations, row echelon forms, rank, invertible and symmetric matrices, determinant and its properties.
Vector Spaces: definitions, examples, subspaces, sum, and intersection.
Systems of Vectors: linear dependence, independence, span, bases, and dimension.
Changes of Basis and Coordinates: Grassmann's formula and direct sum.
Linear Maps (Linear Transformations): kernel, image, composition, isomorphisms, matrix representation.
Endomorphisms: eigenvalues, eigenvectors, characteristic polynomial, diagonalization.
Inner Products: orthogonal bases, norm, spectral theorem, diagonalization of symmetric matrices.
Practical Exercises and Applications on the covered topics.
Programme
SyllabusTentative Course Schedule
Sets and Functions: numerical sets, Cartesian product, domain, codomain, graphs, and properties (injective, surjective, invertible).
Linear Systems: definition, geometric interpretation, solution methods, Gauss elimination algorithm.
Matrices: operations, row echelon forms, rank, invertible and symmetric matrices, determinant and its properties.
Vector Spaces: definitions, examples, subspaces, sum, and intersection.
Systems of Vectors: linear dependence, independence, span, bases, and dimension.
Changes of Basis and Coordinates: Grassmann's formula and direct sum.
Linear Maps (Linear Transformations): kernel, image, composition, isomorphisms, matrix representation.
Endomorphisms: eigenvalues, eigenvectors, characteristic polynomial, diagonalization.
Inner Products: orthogonal bases, norm, spectral theorem, diagonalization of symmetric matrices.
Practical Exercises and Applications on the covered topics.
Core Documentation
Abate-de Fabritiis, Geometria analitica con elementi di algebra lineare, ed. McGraw-Hill, IV edizione. Lecture notes.Reference Bibliography
Abate-de Fabritiis, Geometria analitica con elementi di algebra lineare, ed. McGraw-Hill.Type of evaluation
Written and oral examination. The possibility of holding intermediate exams (midterms) that may exempt students from the written exam will be evaluated.Canali
teacher profile teaching materials
Tentative Course Schedule
Sets and Functions: numerical sets, Cartesian product, domain, codomain, graphs, and properties (injective, surjective, invertible).
Linear Systems: definition, geometric interpretation, solution methods, Gauss elimination algorithm.
Matrices: operations, row echelon forms, rank, invertible and symmetric matrices, determinant and its properties.
Vector Spaces: definitions, examples, subspaces, sum, and intersection.
Systems of Vectors: linear dependence, independence, span, bases, and dimension.
Changes of Basis and Coordinates: Grassmann's formula and direct sum.
Linear Maps (Linear Transformations): kernel, image, composition, isomorphisms, matrix representation.
Endomorphisms: eigenvalues, eigenvectors, characteristic polynomial, diagonalization.
Inner Products: orthogonal bases, norm, spectral theorem, diagonalization of symmetric matrices.
Practical Exercises and Applications on the covered topics.
Programme
SyllabusTentative Course Schedule
Sets and Functions: numerical sets, Cartesian product, domain, codomain, graphs, and properties (injective, surjective, invertible).
Linear Systems: definition, geometric interpretation, solution methods, Gauss elimination algorithm.
Matrices: operations, row echelon forms, rank, invertible and symmetric matrices, determinant and its properties.
Vector Spaces: definitions, examples, subspaces, sum, and intersection.
Systems of Vectors: linear dependence, independence, span, bases, and dimension.
Changes of Basis and Coordinates: Grassmann's formula and direct sum.
Linear Maps (Linear Transformations): kernel, image, composition, isomorphisms, matrix representation.
Endomorphisms: eigenvalues, eigenvectors, characteristic polynomial, diagonalization.
Inner Products: orthogonal bases, norm, spectral theorem, diagonalization of symmetric matrices.
Practical Exercises and Applications on the covered topics.
Core Documentation
Abate-de Fabritiis, Geometria analitica con elementi di algebra lineare, ed. McGraw-Hill, IV edizione. Lecture notes.Reference Bibliography
Abate-de Fabritiis, Geometria analitica con elementi di algebra lineare, ed. McGraw-Hill.Type of evaluation
Written and oral examination. The possibility of holding intermediate exams (midterms) that may exempt students from the written exam will be evaluated.Canali
teacher profile teaching materials
Tentative Course Schedule
Sets and Functions: numerical sets, Cartesian product, domain, codomain, graphs, and properties (injective, surjective, invertible).
Linear Systems: definition, geometric interpretation, solution methods, Gauss elimination algorithm.
Matrices: operations, row echelon forms, rank, invertible and symmetric matrices, determinant and its properties.
Vector Spaces: definitions, examples, subspaces, sum, and intersection.
Systems of Vectors: linear dependence, independence, span, bases, and dimension.
Changes of Basis and Coordinates: Grassmann's formula and direct sum.
Linear Maps (Linear Transformations): kernel, image, composition, isomorphisms, matrix representation.
Endomorphisms: eigenvalues, eigenvectors, characteristic polynomial, diagonalization.
Inner Products: orthogonal bases, norm, spectral theorem, diagonalization of symmetric matrices.
Practical Exercises and Applications on the covered topics.
Programme
SyllabusTentative Course Schedule
Sets and Functions: numerical sets, Cartesian product, domain, codomain, graphs, and properties (injective, surjective, invertible).
Linear Systems: definition, geometric interpretation, solution methods, Gauss elimination algorithm.
Matrices: operations, row echelon forms, rank, invertible and symmetric matrices, determinant and its properties.
Vector Spaces: definitions, examples, subspaces, sum, and intersection.
Systems of Vectors: linear dependence, independence, span, bases, and dimension.
Changes of Basis and Coordinates: Grassmann's formula and direct sum.
Linear Maps (Linear Transformations): kernel, image, composition, isomorphisms, matrix representation.
Endomorphisms: eigenvalues, eigenvectors, characteristic polynomial, diagonalization.
Inner Products: orthogonal bases, norm, spectral theorem, diagonalization of symmetric matrices.
Practical Exercises and Applications on the covered topics.
Core Documentation
Abate-de Fabritiis, Geometria analitica con elementi di algebra lineare, ed. McGraw-Hill, IV edizione. Lecture notes.Reference Bibliography
Abate-de Fabritiis, Geometria analitica con elementi di algebra lineare, ed. McGraw-Hill.Type of evaluation
Written and oral examination. The possibility of holding intermediate exams (midterms) that may exempt students from the written exam will be evaluated.