Talk:Determinant

Yeah, I'm going to retool this article. Doesn't ever give the way a matrix is calculated (cases listed are special cases)

The determinant is equal to the product of the eigenvalues of a matrix.

That isn't true, espcecially as in the definition of eigenvalue, you are talking only about real vector spaces. Example:

<math>\begin{pmatrix} 1 & 0 & 0 \\ 0 & 0 & 2 \\ 0 & -2 & 0 \end{pmatrix}</math>.

• Eigenvalues: 1
• Determinant: 4

FrankC aka ComedyFan 14:29, 2 May 2010 (EDT)

The other problem:

<math>\begin{pmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \\ \end{pmatrix}</math>

• Eigenvalues: 2
• Determinant: 8

The algebraic multiplicity has to be taken into account, the simple sentence the determinant is equal to the product of the eigenvalues of a matrix was misleading. FrankC aka ComedyFan 08:49, 5 May 2010 (EDT)