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It will be possible to replace the written exam by two partial tests, one half-way through the course and one at the end of the course.
Matrix calculus, invertible matrices. Rank of a matrix. Algebraic properties of matrices.
Vector spaces, subspaces, linear dependence, bases. Dimension of a vector space.
Sums of vector spaces, intersection of vector spaces.
Linear maps. Kernel and image of a linear map. Matrix of a linear map. Matrix associated with a change of basis. Duality
Determinant of a matrix. Eigenvalues and eigenvectors of a linear map. Diagonalizable matrices. Page-Rank algorithm. Jordan’s theory
The space of geometric vectors: inner product and its properties, the norm of a vector, Schwarz inequality.
Quadratic forms. Symmetric bilinear forms. Spectral theorem for real symmetric matrices.
Affine spaces and subvarieties. Affine coordinates. Affine transformations. Euclidean space. Isometries. Parallel, incident and skew subvarieties. Distance, angles. Volume of parallelepipeds: explicit formulas.
– A. Bernardi, A. Gimigliano – Algebra lineare e geometria analitica
(Seconda edizione) – 2018 – ISBN:
9788825174243
– Notes from the instructor
