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Linear Algebra

Exercise 6.7.11

Answers

1.

Since

T

is normal, we have that

T^{∗} (x) = \bar{λ} x

if

T (x) = λx

. Hence we know that the eigenvalues of

T^{∗} T

are

| λ_{1} |^{2}, | λ_{2} |^{2}, \dots, | λ_{n} |^{2} .

So we know the singular values are

| λ_{1} |, | λ_{2} |, \dots, | λ_{n} | .

2.

Replace

T

by

A

.

jephianlin

2011-06-27 00:00

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