Content deleted Content added
→Signed permutation group: prop, orthogonal group |
m +2. |
||
Line 5:
0 & -2 & 0 & 0\\
1 & 0 & 0 & 0\\
0 & 0 & 0 & 1\end{bmatrix}.</math>
A [[nonsingular]] matrix ''A'' is a generalized permutation matrix if and only if it can be written as a product of a nonsingular [[diagonal matrix]] ''D'' and a [[permutation matrix]] ''P'':
:<math> A=DP. </math>
An interesting theorem states the following: If a nonsingular matrix and its inverse are both nonnegative matrices (i.e. matrices with nonnegative entries), then the matrix is a generalized permutation matrix.
| |||