Acquire a good knowledge of the theory of bilinear forms and their geometric applications. An important application will be the study of Euclidean geometry, mainly in the plane and in the space, and the Euclidean classification of the conics and of the quadratic surfaces.
Curriculum
scheda docente
materiale didattico
Marco Manetti, Algebra lineare, per matematici.
Serge Lang, Algebra Lineare, Bollati Boringhieri.
Programma
Symmetric and skew-symmetric bilinear forms. Orthogonal and symplectic transformations. Scalar products and Hermitian products. The Spectral Theorem for Hemitian, symmetric and normal operators. Affine and projective spaces. Classification of affine, euclidean and projective conics and quadrics.Testi Adottati
E. Sernesi: Geometria 1 Bollati Boringhieri, 2000.Marco Manetti, Algebra lineare, per matematici.
Serge Lang, Algebra Lineare, Bollati Boringhieri.
Modalità Erogazione
Frontal lessons and exercises.Modalità Frequenza
Attending lessons is strongly suggested.Modalità Valutazione
Before of the oral exam, one should pass either the written exam or the midterms.
scheda docente
materiale didattico
Marco Manetti, Algebra lineare, per matematici.
Serge Lang, Algebra Lineare, Bollati Boringhieri.
Programma
Symmetric and skew-symmetric bilinear forms. Orthogonal and symplectic transformations. Scalar products and Hermitian products. The Spectral Theorem for Hemitian, symmetric and normal operators. Affine and projective spaces. Classification of affine, euclidean and projective conics and quadrics.Testi Adottati
E. Sernesi: Geometria 1 Bollati Boringhieri, 2000.Marco Manetti, Algebra lineare, per matematici.
Serge Lang, Algebra Lineare, Bollati Boringhieri.
Modalità Erogazione
Frontal lessons and exercises.Modalità Frequenza
Attending lessons is strongly suggested.Modalità Valutazione
Before of the oral exam, one should pass either the written exam or the midterms.