Linear Algebra and Its Applications · Problem 7.2.11

Computations with Matrices — Gilbert Strang

Mathematics · condition-number

Problem

(a) Do

A

and

A^{-1}

have the same condition number

c

? (b) In parallel with the upper bound (8) on the error, prove a lower bound:

\frac{\|\delta x\|}{\|x\|} \geq \frac{1}{c} \frac{\|\delta b\|}{\|b\|}. \qquad \text{(Consider } A^{-1}b = x \text{ instead of } Ax = b.)