Relation between eigenvalue and singular value
July 11, 2016
For any square matrix A, we have
where are the singular values, and
are the eigenvalues.
Proof of the right half of the inequality:
See Topics in matrix analysis: page 151, Corollary 3.1.5
Proof of the left half of the inequality:
First, we have
To verify, it is easy to see and
.
Second, applying the right half of the inequality gives
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