Under such circumstance P will be a unitary matrix (resp.
All eigenvalues of an unitary matrix lie on the unit circle.
The real analogue of a unitary matrix is an orthogonal matrix.
Any square matrix with unit Euclidean norm is the average of two unitary matrices.
Every eigenvalue of a unitary matrix has absolute value .
As for a single matrix, over the complex numbers these can be triangularized by unitary matrices.
The isometric linear maps from C to itself are the unitary matrices.
Despite the name, matrix units are not the same as unit matrices or unitary matrices.
It is not impossible that the connection with random unitary matrices could lead to a proof of Riemann hypothesis.
U is an arbitrary unitary matrix, a complex rotation in phase space.