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. 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