3. Let A be mxnand B be nxm. a) Show that the matrices C = 0 0 B BA b) Conclude that the nonzero eigenvalues of AB are the same as those of BA. AB O B 0 a and D= are similar.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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3. Let A be mxnand B be nxm.
a) Show that the matrices C-
0
0
8) a
0
B BA
b) Conclude that the nonzero eigenvalues of AB are the same as those of BA.
AB
B
and D=
are similar.
Transcribed Image Text:3. Let A be mxnand B be nxm. a) Show that the matrices C- 0 0 8) a 0 B BA b) Conclude that the nonzero eigenvalues of AB are the same as those of BA. AB B and D= are similar.
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