# Adjoint matrix

From Encyclopedia of Mathematics

*Hermitian adjoint matrix, of a given (rectangular or square) matrix over the field of complex numbers*

The matrix whose entries are the complex conjugates of the entries of , i.e. . Thus, the adjoint matrix coincides with its complex-conjugate transpose: where denotes complex conjugation and the denotes transposition.

Properties of adjoint matrices are:

Adjoint matrices correspond to adjoint linear transformations of unitary spaces with respect to orthonormal bases.

For references, see Matrix.

**How to Cite This Entry:**

Adjoint matrix. T.S. Pogolkina (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Adjoint_matrix&oldid=12893

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098