2] are

unitary matrices, and the diagonal matrices [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] have nonnegative diagonal entries satisfying [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

ultra] is rank-structured and

unitary matrices preserve rank.

then there exist

unitary matrices U [member of] U [C.

This facsimile of the 1950 edition by Clarendon Press includes all the original material, covering matrices, algebras, groups, the Frobenius algebra, the symmetric group, immanants and S-functions, the S-functions of special series, the calculation of the characters of the symmetric group, group characters and the construction of groups, continuous matrix groups and invariant matrices, and groups of

unitary matrices.

Killip and Nenciu [26] describe an ensemble of n x n random

unitary matrices whose eigenvalues are distributed according to the Gibbs distribution for n particles of the Coulomb gas on the unit circle.

The CMV and

unitary matrices in general are linked to orthogonal polynomials on the unit circle for which a rich variety of literature is available; early contributions and references can be found in [1-3].

which, for

unitary matrices, links closely to CMV matrices [32].

where U and V are

unitary matrices, and [SIGMA] is a diagonal matrix where the diagonal entries are real and nonnegative and satisfy [[sigma].

At each iteration, there exist

unitary matrices [V.

A singular value decomposition of a non-zero complex N x N matrix B is an expression of B as a product B = V[SIGMA]W*, where V and W are

unitary matrices in [C.

A quantum computation applies a unitary matrix to a vector [5], and quantum (logic) circuits are a notational shorthand for factorizations of such

unitary matrices into more basic ones, corresponding to gates.

Unitary matrices A are characterized by [parallel] Ax [parallel] = [parallel] x [parallel] for all x [member of] [H.