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In [[mathematics]], the '''conjugate transpose''' or '''Hermitian transpose''' of an ''m''-by-''n'' [[matrix (mathematics)|matrix]] <math>\boldsymbol{A}</math> with [[complex number|complex]] entries is the ''n''-by-''m'' matrix <math>\boldsymbol{A}^\mathrm{H}</math> obtained from <math>\boldsymbol{A}</math> by taking the [[transpose]] and then taking the [[complex conjugate]] of each entry. (The complex conjugate of <math>a+ib</math> is <math>a-ib</math>, for real numbers <math>a</math> and <math>b</math>.)
For real matrices the conjugate transpose is just the transpose, <math>\boldsymbol{A}^\mathrm{H} = \boldsymbol{A}^\
==Definition==
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