In conclusion, the unitary matrices which are linear combinations of permutation matrices are precisely the unitary matrices which have v as an eigenvector.
Are permutation matrices Nonsingular?
A permutation matrix is a square matrix obtained from the same size identity matrix by a permutation of rows. Such a matrix is always row equivalent to an identity. ... Since interchanging two rows is a self-reverse operation, every elementary permutation matrix is invertible and agrees with its inverse, P = P−1 or P2 = I.
Is a permutation matrix orthogonal?
Definition 1-7.
It can be shown that every permutation matrix is orthogonal, i.e., PT = P−1.
