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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 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> being <math>a-ib</math>, for real numbers <math>a</math> and <math>b</math>). It is often denoted as <math>\boldsymbol{A}^\mathrm{H}</math> or <math>\boldsymbol{A}^*</math>.<ref name=":1">{{Cite web|last=Weisstein|first=Eric W.|title=Conjugate Transpose|url=https://mathworld.wolfram.com/ConjugateTranspose.html|access-date=2020-09-08|website=mathworld.wolfram.com|language=en}}</ref><ref name=":2">{{Cite web|title=conjugate transpose|url=https://planetmath.org/ConjugateTranspose|access-date=2020-09-08|website=planetmath.org}}</ref>
For [[Real number|real]] matrices, the conjugate transpose is just the transpose, <math>\boldsymbol{A}^\mathrm{H} = \boldsymbol{A}^\mathsf{T}</math>.
==Definition==
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