Prove that the stated property is a similarity invariant. Trace

driliwra7

driliwra7

Answered question

2022-09-09

Prove that the stated property is a similarity invariant. Trace

Answer & Explanation

Yasmin Lam

Yasmin Lam

Beginner2022-09-10Added 13 answers

Suppose A and B are two similarity invariant matrices, and B = P 1 A P.
t r ( A B ) = t r ( B A )
t r ( B ) = t r ( P 1 A P )
= t r ( P 1 ( A P ) )
= t r ( ( A P ) P 1 )
= t r ( A ( P P 1 ) )
=tr(A)
Trace of matrix is similarity invariant.
Result:
Use tr(AB)=tr(BA) for A , B M n n .

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