Conjugate transpose: Difference between revisions

Revision as of 08:55, 21 April 2005

Revision as of 09:58, 21 April 2005

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* (''A'' + ''B'')^* = ''A''^* + ''B''^* for any two matrices ''A'' and ''B'' of the same format.

* (''rA'')^* = ''r''^*''A''^* for any complex number ''r'' and any matrix ''A''. Here ''r''^* refers to the complex conjugate of ''r''.

* (''AB'')^* = ''B''^*''A''^* for any ''m''-by-''n'' matrix ''A'' and any ''n''-by-''p'' matrix ''B''. Note that the orerorder of the factors is reversed.

* (''A''^*)^* = ''A'' for any matrix ''A''.

* If ''A'' is a square matrix, then [[determinant|det]] (''A''^*) = (det A)^* and [[trace (matrix)|trace]] (''A''^*) = (trace A)^*