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Invertible matrices and their characterization by the rank. Gauss-Jordan algorithm for computing the inverse of a matrix. Square systems of linear equations. Cramer theorem. Homogeneous systems and their space of solutions. Determinant of a matrix: definition and properties. How to compute the determinant by the gauss algorithm.
Vector spaces: definition and elementary properties. Subspaces. Span of subset of vectors. Intersection and sum of subspaces. Direct sum. Linear dependence and linear independence. Bases and dimension of a vector space. Grassmann identity.
Linear maps. Kernel and image of a linear map. Link between their dimensions. Matrices associated with a linear map.
M. Barnabei – F. Bonetti:
Spazi Vettoriali e Trasformazioni lineari
Pitagora, Bologna, 1993
Sistemi Lineari e Matrici
Pitagora, Bologna, 2003