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How can I find the determinant of the conjugate matrix?

  • Thread starter ptolema
  • Start date
1. The problem statement, all variables and given/known data

conj.jpg


2. Relevant equations

complex conjugate of a+bi is a-bi

3. The attempt at a solution

I defined M = A+Bi, where A and B contain real number entries. So that means that [tex]\bar{}M[/tex] = A-Bi. Past that point, I don't know what to do. How can I find the determinant of the conjugate matrix? Or the complex conjugate of det (M)? Could someone give me a hand?
 
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I like Serena

Homework Helper
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Re: determinant

I'd say that the determinant of a matrix is a bunch of additions on products of complex numbers which make up the matrix.

Note that when you multiply or add 2 conjugate numbers, the result is the same when you multiply or add the original numbers and then take the conjugate.

So the determinant of a conjugated matrix has to be the same as the conjugate of the determinant of a matrix.
 
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Re: determinant

I think using induction and then doing a cofactor expansion would work, though I haven't checked the details.
 

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