Linear Algebra and Its Applications · Problem 7.2.15

Computations with Matrices — Gilbert Strang

Mathematics · condition-number-orthogonal

Problem

Why is

I

the only symmetric positive definite matrix that has

\lambda_{\max} = \lambda_{\min} = 1

? Then the only matrices with

\|A\| = 1

and

\|A^{-1}\| = 1

must have

A^TA = I

. They are \underline{\hspace{1cm}} matrices.