Unitary Matrix

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unitary matrix

[′yü·nə‚ter·ē ′mā·triks]
A matrix whose inverse is equal to the complex conjugate of its transpose.

Unitary Matrix


A unitary matrix of order n is an n × n matrix [uik] with complex entries such that the product of [uik] and its conjugate transpose [ūki] is the identity matrix E. The elements of a unitary matrix satisfy the relations

The unitary matrices of order n form a group under multiplication. A unitary matrix with real entries is an orthogonal matrix.

References in periodicals archive ?
1), we form [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] partitioned analogously and let V be a unitary matrix such that
N] and the set of all unitary matrix functions by U[M.
The [E] matrix can be found as a matrix that previously consists of the unitary matrix of the dimension of n x n and a null rectangular matrix of the dimension of N x n.
Any unitary matrix U with width (U) = c may be written as
The sample points are the eigenvalues of a certain unitary matrix, and the weights are the squares of the absolute values of the first components of the eigenvectors.
The QR decomposition of a Hessenberg matrix is structured, since the unitary matrix Q is the product of n - 1 rotators in a descending order, e.
Construct a unitary matrix U which takes [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] into Schur form
If the unitary matrix Q admits a decomposition into at most n-1 rotations all acting on different pairs of neighboring rows, then we will call A an extended Hessenberg matrix.
Now we construct a unitary matrix U which has x as its first column, U = [x, [U.
Clearly, any unitary matrix U which satisfies U[SIGMA] = [SIGMA]U defines another SVD of B, namely, B = (VU)[SIGMA](WU)*.
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.
U is an unitary matrix given by U = F[OMEGA], F is the Fourier matrix