Express $det(A \otimes A)$ using trace and det of $A$. I know that determinant is product of eigenvalues, and trace is sum. But i cannot procceed further. Any hints?
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What is $A$? What does $\otimes$ mean here? – Eric Wofsey Dec 16 '19 at 21:34
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@EricWofsey $\otimes$ means tensor product. A is a linear operator – friendlyuser Dec 16 '19 at 21:35
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1What do you mean by "tensor product"? How are you tensoring a scalar and a linear operator? – Eric Wofsey Dec 16 '19 at 21:35
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Is it possible you meant $det(A\otimes A)$? – Captain Lama Dec 16 '19 at 21:38
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@CaptainLama yes, i will edit – friendlyuser Dec 16 '19 at 21:39
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1Can you find a formula in the case where $A$ is diagonalizable? – Captain Lama Dec 16 '19 at 21:40
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It is very bad form to just start using a variable without saying what it is. To be completely clear, is the following correct? You have a finite-dimensional vector space $V$, a linear map $A:V\to V$, and you are asking to find a formula for the determinant of the map $A\otimes A:V\otimes V\to V\otimes V$? (Don't comment, add these details to your question!) – Eric Wofsey Dec 16 '19 at 21:41