(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

1) two linear transformations B and C are equivalent iff there exist invertible linear transformations P and Q such that PB=CQ

2) if A and B are equivalent then so are A' and B' in dual space

3) Do there exist linear transformations A and B such that A and B are equivalent but A^2 and B^2 are not?

4) Does there exist a linear transformation A such that A is equivalent to a scalar a but A is not equal to a?

3. The attempt at a solution

I really don't know where to start. I know that if two l.ts. A and B are equivalent then (AB)^-1 = B^-1A^-1. But that's where I am now.

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# Homework Help: Linear algebra: equivalence

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