permutationlike
Permutationlike is a term used in linear algebra to describe square matrices that are similar to permutation matrices. A matrix A is permutationlike if there exists an invertible matrix S and a permutation matrix P with A = S^{-1} P S. In other words, A represents, in some basis, a permutation of the standard basis vectors.
Key properties: Since permutation matrices are diagonalizable over the complex numbers with eigenvalues that are roots
Characterizations and constraints: Permutationlike matrices are exactly those matrices that are similar to a permutation matrix.
Examples and non-examples: The identity matrix is permutationlike. Any matrix similar to a cycle permutation matrix