Adjoint matrix
From Encyclopedia of Mathematics
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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. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Adjoint_matrix&oldid=12893
Adjoint matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Adjoint_matrix&oldid=12893
This article was adapted from an original article by T.S. Pogolkina (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article