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→Definition: Added a fact that an entry is a matrix element, and explicitly mentioned one important name of conjugate transpose in a middle of this Wikipedia page even if it is mentioned in the introductory section once. |
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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
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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
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