1. Show that the decomposition of an upper Hessenberg matrix using Givens rotations costs 2 flops. 2. 3. Show that an orthogonal similarity transformation maintains the condition number of an...

1.

Show that the

decomposition of an upper Hessenberg matrix using Givens rotations costs


²

flops.

2.

3.

Show that an orthogonal similarity transformation maintains the condition number of an eigenvalue.

A real matrix is said to be normal if

<sup>T

T</sup>

Problems
deal with properties of a normal matrix.