## 20410335 - GE110 - Geometry and linear algebra 1

Acquire a good knowledge of the concepts and methods of basic linear algebra, with particular attention given to the study of linear systems, matrices and determinants, vector spaces and linear applications, affine geometry.

Curriculum

teacher profile | teaching materials

Programme

Vector spaces and subspaces. Matrices. Row by column multiplication. Gaussian elimination and homogenous linear systems. Generators of a vector space end linearly independent vectors. Basis and dimension of a vector space. Grassmann Formula. Rank of a matrix and invertible matrices. Rouché-Capelli Theorem and solutions of a linear system. Determinant. Linear maps. Kernel and image of a linear map. The nullity plus rank theorem. Matrix associated to a linear map. Change of basis. Dual vector space and transpose of a linear map. diagonalization of linear operators. Minimal polynomial. Jordan canonical form.

Core Documentation

Marco Manetti, Algebra lineare, per matematici.
Serge Lang, Algebra Lineare, Bollati Boringhieri.
Edoardo Sernesi, Geometria I, Bollati Boringhieri.

Type of delivery of the course

Lectures and exercise classes

Type of evaluation

There will be two midterm tests, the successful completion of which will exempt fro the written part of the exam.

teacher profile | teaching materials

Programme

Vector spaces and subspaces. Matrices. Row by column multiplication. Gaussian elimination and homogenous linear systems. Generators of a vector space end linearly independent vectors. Basis and dimension of a vector space. Grassmann Formula. Rank of a matrix and invertible matrices. Rouché-Capelli Theorem and solutions of a linear system. Determinant. Linear maps. Kernel and image of a linear map. The nullity plus rank theorem. Matrix associated to a linear map. Change of basis. Dual vector space and transpose of a linear map. diagonalization of linear operators. Minimal polynomial. Jordan canonical form.

Core Documentation

Marco Manetti, Algebra lineare, per matematici.
Serge Lang, Algebra Lineare, Bollati Boringhieri.
Edoardo Sernesi, Geometria I, Bollati Boringhieri.

Type of delivery of the course

Lectures and exercise classes

Type of evaluation

There will be two midterm tests, the successful completion of which will exempt fro the written part of the exam.