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Sequel to MA 6013, basics concepts of linear algebra and matrix theory. Linear mappings their range and null spaces, tensor product of transformations, determinants, eigenvalues, multiplicities, triangular form, nilpotence, Jordan form, inner products, inner product spaces, orthogonality, completeness Schwarz's inequality, complete orthonormal sets, the projection theorem, linear functionals,self-adjoint transformations, polarization, positive transformations, isometries, change of orthonormal basis, characterization of spectra, the spectral theorem, normal transformations, orthogonal transformations, functions of transformations, polar decomposition, commutativity. Applications for matrices and for di®erential equations.