Let A have singular values 1, n Prove that ATA is a convergent matrix if and only if 1 1 (Later we will show that this implies that A itself is convergent )

Question: Let A have singular values 1, > > n. Prove that ATA is a convergent matrix if and only if 1 <

Let A have singular values σ1, > ∙ ∙ ∙ > σn. Prove that ATA is a convergent matrix if and only if σ1 < 1. (Later we will show that this implies that A itself is convergent.)

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