Unitary matrix in trace and log function I am

Adison Palmer

Adison Palmer

Answered question

2022-04-11

Unitary matrix in trace and log function
I am trying to do a unitary transformation U on square matrix A which is embedded inside a trace and natural log function, and the following property is supposed to hold:
tr(ln(A))=tr(ln(UAU))
What property of the tr and ln  functions would allow us to do that?

Answer & Explanation

Austin Sherman

Austin Sherman

Beginner2022-04-12Added 12 answers

A corollary of Jacobi's formula for invertible matrices is
trlogX=logdetX
Applying it to this problem yields
trlog(UAU)=logdet(UAU)
=logdet(A)
=trlog(A)

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