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

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
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3. Let A be mxn and B be nxm.
0 0
a) Show that the matrices C=
B BA
b) Conclude that the nonzero eigenvalues of AB are the same as those of BA.
Suppoco that 1 and 2 ore distinot sigenvalues of matrix 1 with oorrogponding
AB
B
and D=
are similar.
Transcribed Image Text:3. Let A be mxn and B be nxm. 0 0 a) Show that the matrices C= B BA b) Conclude that the nonzero eigenvalues of AB are the same as those of BA. Suppoco that 1 and 2 ore distinot sigenvalues of matrix 1 with oorrogponding AB B and D= are similar.
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