All eigenvalues of an unitary matrix lie on the unit circle.

Under such circumstance P will be a unitary matrix (resp.

U is an arbitrary unitary matrix, a complex rotation in phase space.

Every eigenvalue of a unitary matrix has absolute value .

The isometric linear maps from C to itself are the unitary matrices.

As for a single matrix, over the complex numbers these can be triangularized by unitary matrices.

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.

For any unitary matrix U, the following hold:

Since the rows of the matrix are orthogonal, 'H' is indeed a unitary matrix.

Despite the name, matrix units are not the same as unit matrices or unitary matrices.

A is diagonalizable by a unitary matrix.

One major example of this uses an orthogonal or unitary matrix, and a triangular matrix.

It is not impossible that the connection with random unitary matrices could lead to a proof of Riemann hypothesis.

The kernel of this homomorphism is the set of unitary matrices with determinant 1.

Since the transformation is by a unitary matrix the normalization of the real and the complex solid harmonics is the same.

Using the permutation maps it is possible to verify directly that a set of unitary matrices forms a t-design.

(Note that there are N independent eigenvectors; a unitary matrix is never defective.)

The proof uses random unitary matrices.

Since the productof two unitary matrices is unitary, the proof is done.

The circle group is also the group U(1) of 1x1 unitary matrices; these act on the complex plane by rotation about the origin.

Isometrical isomorphisms are also known as unitary operators (compare with unitary matrix).

In quantum information, single-qubit quantum gates are 2 x 2 unitary matrices.

Orthogonal matrices are the special case of unitary matrices in which all entries are real.

The analogous complex-valued matrices are the unitary matrices.