Editing Conjugate transpose (section)

==Definition==
The conjugate transpose of an <math>m \times n</math> matrix <math>\mathbf{A}</math> is formally defined by
{{Equation box 1
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|equation = {{NumBlk||<math>\left(\mathbf{A}^\mathrm{H}\right)_{ij} = \overline{\mathbf{A}_{ji}}</math>|{{EquationRef|Eq.1}}}}
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|border colour = #0073CF
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where the subscript <math>ij</math> denotes the <math>(i,j)</math>-th entry (matrix element), for <math>1 \le i \le n</math> and <math>1 \le j \le m</math>, and the overbar denotes a scalar complex conjugate.

This definition can also be written as
:<math>\mathbf{A}^\mathrm{H} = \left(\overline{\mathbf{A}}\right)^\operatorname{T} = \overline{\mathbf{A}^\operatorname{T}}</math>

where <math>\mathbf{A}^\operatorname{T}</math> denotes the transpose and <math>\overline{\mathbf{A}}</math> denotes the matrix with complex conjugated entries.

Other names for the conjugate transpose of a matrix are '''Hermitian transpose''', '''Hermitian conjugate''', '''adjoint matrix''' or '''transjugate'''. The conjugate transpose of a matrix <math>\mathbf{A}</math> can be denoted by any of these symbols:
* <math>\mathbf{A}^*</math>, commonly used in [[linear algebra]]
* <math>\mathbf{A}^\mathrm{H}</math>, commonly used in linear algebra
* <math>\mathbf{A}^\dagger</math> (sometimes pronounced as ''A [[dagger (typography)|dagger]]''), commonly used in [[quantum mechanics]]
* <math>\mathbf{A}^+</math>, although this symbol is more commonly used for the [[Moore–Penrose pseudoinverse]]

In some contexts, <math>\mathbf{A}^*</math> denotes the matrix with only complex conjugated entries and no transposition.