# Unitary Matrix

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## unitary matrix

[′yü·nə‚ter·ē ′mā·triks] (mathematics)

A matrix whose inverse is equal to the complex conjugate of its transpose.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

The following article is from

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.## Unitary Matrix

A unitary matrix of order *n* is an *n* × *n* matrix [*u _{ik}*] with complex entries such that the product of [

*u*] and its conjugate transpose [

_{ik}*ū*] is the identity matrix

_{ki}*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.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.