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Presentation. Use of mathematical notation for matrix dimensions. Tags: Visual edit Disambiguation links added |
m Add A' notation that goes back to at least 1934 and is in common use today as well. |
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{{redirect|Adjoint matrix|the transpose of cofactor|Adjugate matrix}}
In [[mathematics]], the '''conjugate transpose''', also known as the '''Hermitian transpose''', of an <math>m \times n</math> [[Complex number|complex]] [[matrix (mathematics)|matrix]] <math>\boldsymbol{A}</math> is an <math>n \times m</math> matrix obtained by [[transposing]] <math>\boldsymbol{A}</math> and applying [[complex conjugate]] on 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>
or
<math>\boldsymbol{A}'</math>
<ref>
H. W. Turnbull, A. C. Aitken,
"An Introduction to the Theory of Canonical Matrices,"
1934.
</ref>.
For [[Real number|real]] matrices, the conjugate transpose is just the transpose, <math>\boldsymbol{A}^\mathrm{H} = \boldsymbol{A}^\mathsf{T}</math>.
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