Linear Algebra and Its Applications · Problem 7.2.13

Computations with Matrices — Gilbert Strang

Mathematics · matrix-norm-condition-number

Problem

Find the norms and condition numbers from the square roots of

\lambda_{\max}(A^TA)

and

\lambda_{\min}(A^TA)

\begin{bmatrix} -2 & 0 \\ 0 & 2 \end{bmatrix} \qquad \begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix} \qquad \begin{bmatrix} 1 & 1 \\ -1 & 1 \end{bmatrix}.