Programma

Matrices - Linear systems - Vector Spaces - Subspaces - Bases - Dimension - Rank - Determinants - Affine Spaces - Subspaces - Geometry in an affine plane - Geometry in an affine space of dimension 3 - Linear maps - Matrices and linear maps - Change of coordinates - Linear operators and square matrices - Eigenvectors, eigenvalues and their computation - Diagonalization of linear operators and of square matrices via the study of eigenspaces.

Testi Adottati

E. Sernesi: Geometria I, Bollati Boringhieri (1989)

Modalità Frequenza

mandatory

Modalità Valutazione

Two midterms that consist of 3 exercises in 2 and a half hours. If passed, the student is admitted to the oral exam. Written exam: solution of 3 exercises in 3 hours. Oral exam: verification of knowledge of concepts and results done in the course. Written exams and midterms of previous years can be found in the webpage of the teacher http://ricerca.mat.uniroma3.it/users/lopez/corsi.html In evaluating the exam, the determination of the final grade will take into account the following elements: written grade, level and quality of knowledge of the topics; the ability to critically analyze a topic; the logic of the arguments supporting a thesis; the ability to apply theories and concepts to contexts; the use of vocabulary appropriate to the discipline being studied.

Programma

Matrices - Linear systems - Vector Spaces - Subspaces - Bases - Dimension - Rank - Determinants - Affine Spaces - Subspaces - Geometry in an affine plane - Geometry in an affine space of dimension 3 - Linear maps - Matrices and linear maps - Change of coordinates - Linear operators and square matrices - Eigenvectors, eigenvalues and their computation - Diagonalization of linear operators and of square matrices via the study of eigenspaces.

Programma

Matrices - Linear systems - Vector Spaces - Subspaces - Bases - Dimension - Rank - Determinants - Affine Spaces - Subspaces - Geometry in an affine plane - Geometry in an affine space of dimension 3 - Linear maps - Matrices and linear maps - Change of coordinates - Linear operators and square matrices - Eigenvectors, eigenvalues and their computation - Diagonalization of linear operators and of square matrices via the study of eigenspaces.

Testi Adottati

E. Sernesi: Geometria I, Bollati Boringhieri (1989)

Modalità Frequenza

mandatory

Modalità Valutazione

Two midterms that consist of 3 exercises in 2 and a half hours. If passed, the student is admitted to the oral exam. Written exam: solution of 3 exercises in 3 hours. Oral exam: verification of knowledge of concepts and results done in the course. Written exams and midterms of previous years can be found in the webpage of the teacher http://ricerca.mat.uniroma3.it/users/lopez/corsi.html In evaluating the exam, the determination of the final grade will take into account the following elements: written grade, level and quality of knowledge of the topics; the ability to critically analyze a topic; the logic of the arguments supporting a thesis; the ability to apply theories and concepts to contexts; the use of vocabulary appropriate to the discipline being studied.

Programma

Matrices - Linear systems - Vector Spaces - Subspaces - Bases - Dimension - Rank - Determinants - Affine Spaces - Subspaces - Geometry in an affine plane - Geometry in an affine space of dimension 3 - Linear maps - Matrices and linear maps - Change of coordinates - Linear operators and square matrices - Eigenvectors, eigenvalues and their computation - Diagonalization of linear operators and of square matrices via the study of eigenspaces.