Unitary and Normal Endomorphisms

Jonathan S. Golan ()
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Jonathan S. Golan: University of Haifa, Dept. of Mathematics

Chapter 18 in The Linear Algebra a Beginning Graduate Student Ought to Know, 2012, pp 419-440 from Springer

Abstract: Abstract Unitary endomorphisms of an inner product space are introduced and studied. In particular, unitary and orthogonal matrices are considered. Many examples are considered, among them Householder matrices and special orthogonal matrices. Unitarily-similar matrices are defined and Schur’s Theorem is proven. Normal endomorphisms of an inner product space are also considered and their properties proven, leading up to a proof of the Spectral Decomposition Theorem and the Singular Value Decomposition Theorem.

Keywords: Normal Endomorphism; Singular Value Decomposition Theorem; Special Orthogonal Matrices; Household Matters; Product Space (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-94-007-2636-9_18

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