If A is 6 by 4 and B is 4 by 6, AB and BA have different sizes. Nevertheless, " I A 0 I
Chapter 5, Problem 5.6.43(choose chapter or problem)
If A is 6 by 4 and B is 4 by 6, AB and BA have different sizes. Nevertheless, " I A 0 I #"AB 0 B 0 #"I A 0 I # = " 0 0 B BA# = G. (a) What sizes are the blocks of G? They are the same in each matrix. (b) This equation is M1FM = G, so F and G have the same 10 eigenvalues. F has the eigenvalues of AB plus 4 zeros; G has the eigenvalues of BA plus 6 zeros. AB has the same eigenvalues as BA plus zeros.
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