(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If A is a square symmetric matrix nxn. Show that the determinant of A is the product of its eigenvalues.

2. Relevant equations

3. The attempt at a solution

From spectral decomp.

A = QλQ'

|A| = |QλQ'| = |QQ'λ| = |Q||Q'||λ| = |λ| = the product of its diagonals (eigenvalues).

The step I'm not 100% sure of is if I can interchange QλQ' to QQ'λ

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# Quick linear algebra determinant proof.

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