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The course is linear methods II and the topics are:

Vector spaces, subspaces, independence, basis and dimension,

row and column space of a matrix, rank, applications.

Linear transformations, kernel and image, composition,

linear functionals, the double dual, transpose of a linear transformation.

Orthogonality, Gram-Schmidt process, orthogonal diagonalization and

least squares approximation, quadratic forms, SVD.

Change of basis.

Thanks