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:

${\begin{pmatrix}1&0&0\\0&0&2\\0&-2&0\end{pmatrix}}$.

• Eigenvalues: 1
• Determinant: 4

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

The other problem:

${\begin{pmatrix}2&0&0\\0&2&0\\0&0&2\\\end{pmatrix}}$

• 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)