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Linear Algebra Proof - Determinants and Traces

  • #1
901
3

Homework Statement



Prove for an operator A that det(e^A) = e^(Tr(A))

Homework Equations





The Attempt at a Solution



I have no idea how to start. Can someone give me a hint?

In general the operator A represented by a square matrix, has a trace Tr(A) = Ʃ A (nn) where A (nn) is the nth row nth column. I don't know how to write the determinant in such a form that's understandable to myself and don't know how to compare them.
 

Answers and Replies

  • #2
6,054
390
How about A's Jordan form?
 
  • #3
901
3
I have absolutely no background in linear algebra except a very elementary class on matrix arithmetic/eigenvalue problems and this is part of our "review" for a quantum mechanics class! Very few of my classmates have seen this math before and can't answer, I'm desperate!

Is this possible to solve this using very elementary steps? I've found an advanced proof that I have no idea how to understand. What is a Jordan form?
 
  • #4
6,054
390
The basic idea is that you consider A in the basis of its eigenvectors. Is that enough of a clue?
 
  • #5
901
3
The basic idea is that you consider A in the basis of its eigenvectors. Is that enough of a clue?
Yes I figured it out. thank you greatly.
 

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