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Post Closed as "too localized" by Angelo, Andreas Blass, user9072, Gjergji Zaimi, Harry Gindi
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Turbo
Turbo
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Let $A$ be an $n \times n$ matrix. Are there formulas that convert tracelinear combinations of traces of powers of $A$ to determinant of $A$ and vice versa from determinantlinear combinations of determinants of powers of $A$ to trace of $A$? (I am mainly looking for the latter - conversion of determinants to trace of $A$).

Let $A$ be an $n \times n$ matrix. Are there formulas that convert trace to determinant and vice versa from determinant to trace? (I am mainly looking for conversion of determinants to trace of $A$).

Let $A$ be an $n \times n$ matrix. Are there formulas that convert linear combinations of traces of powers of $A$ to determinant of $A$ and vice versa from linear combinations of determinants of powers of $A$ to trace of $A$? (I am mainly looking for the latter - conversion of determinants to trace of $A$).

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Turbo
Turbo
  • 13.9k
  • 1
  • 27
  • 76

Trace Determinant

Let $A$ be an $n \times n$ matrix. Are there formulas that convert trace to determinant and vice versa from determinant to trace? (I am mainly looking for conversion of determinants to trace of $A$).