I am unable to think of a way to prove this result: Show that every square matrix is a product of a hermitian matrix and an unitary matrix.
I want to prove it using the spectral theorem.
Thanks for the help.
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This is usually done via the "polar decomposition" of a matrix; more information on that is given here. This answer details what that looks like for real matrices; a similar proof applies in the complex case, where the $T$'s are replaced by $*$'s.
Ben Grossmann
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How can the spectral theorem be used to prove it? – Tejas P Sep 01 '17 at 14:05
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The spectral theorem provides a convenient way to show that $A^*A$ has a unique positive definite square root. – Ben Grossmann Sep 01 '17 at 14:17
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Could you please sketch the entire proof? – Tejas P Sep 01 '17 at 14:49
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@TejasP I have no intention of doing so. This is a standard result which you can find in most linear algebra textbooks. – Ben Grossmann Sep 01 '17 at 14:51