Adjoint matrix

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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:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098