Linear Algebra and Its Applications · Problem 7.2.12

Computations with Matrices — Gilbert Strang

Mathematics · matrix-norm-condition-number

Problem

Find the norms

\lambda_{\max}

and condition numbers

\lambda_{\max}/\lambda_{\min}

of these positive definite matrices:

\begin{bmatrix} 100 & 0 \\ 0 & 2 \end{bmatrix} \qquad \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} \qquad \begin{bmatrix} 3 & 1 \\ 1 & 1 \end{bmatrix}.