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
teacher profile teaching materials
Marco Manetti, Algebra lineare, per matematici.
Serge Lang, Algebra Lineare, Bollati Boringhieri.
Programme
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.Core Documentation
E. Sernesi: Geometria 1 Bollati Boringhieri, 2000.Marco Manetti, Algebra lineare, per matematici.
Serge Lang, Algebra Lineare, Bollati Boringhieri.
Type of delivery of the course
Frontal lessons and exercises.Type of evaluation
Before of the oral exam, one should pass either the written exam or the midterms. teacher profile teaching materials
Marco Manetti, Algebra lineare, per matematici.
Serge Lang, Algebra Lineare, Bollati Boringhieri.
Programme
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.Core Documentation
E. Sernesi: Geometria 1 Bollati Boringhieri, 2000.Marco Manetti, Algebra lineare, per matematici.
Serge Lang, Algebra Lineare, Bollati Boringhieri.
Type of delivery of the course
Frontal lessons and exercises.Type of evaluation
Before of the oral exam, one should pass either the written exam or the midterms. teacher profile teaching materials
Marco Manetti, Algebra lineare, per matematici.
Serge Lang, Algebra Lineare, Bollati Boringhieri.
Programme
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.Core Documentation
E. Sernesi: Geometria 1 Bollati Boringhieri, 2000.Marco Manetti, Algebra lineare, per matematici.
Serge Lang, Algebra Lineare, Bollati Boringhieri.
Type of delivery of the course
Frontal lessons and exercises.Type of evaluation
Before of the oral exam, one should pass either the written exam or the midterms. teacher profile teaching materials
Marco Manetti, Algebra lineare, per matematici.
Serge Lang, Algebra Lineare, Bollati Boringhieri.
Programme
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.Core Documentation
E. Sernesi: Geometria 1 Bollati Boringhieri, 2000.Marco Manetti, Algebra lineare, per matematici.
Serge Lang, Algebra Lineare, Bollati Boringhieri.
Type of delivery of the course
Frontal lessons and exercises.Type of evaluation
Before of the oral exam, one should pass either the written exam or the midterms.