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Around the finite-dimensional spectral theorem. (English) Zbl 1012.15007

A direct geometric proof of the singular value decomposition of a (real or complex) linear transformation (of one finite-dimensional inner product space into another) is the starting point of this paper. The singular value decomposition is then used to define and study some classical notions, e.g., adjoint, polar decomposition, spectral theorem, normal forms, etc. This makes the presentation of the above mentioned classical results very natural and simple, which may be appropriate for an introductory course.

MSC:

15A18 Eigenvalues, singular values, and eigenvectors
15A21 Canonical forms, reductions, classification
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