The conjugate transpose of an m×n matrix A is the n×m matrix defined by A^H congruent (A^_)^T, where A^T denotes the transpose of the matrix A and A^_ denotes the conjugate matrix. In all common spaces (i.e., separable Hilbert spaces), the conjugate and transpose operations commute, so A^H congruent (A^_)^T = (A^T)^_. The symbol A^H (where the "H" stands for "Hermitian") gives official recognition to the fact that for complex matrices, it is almost always the case that the combined operation of taking the transpose and complex conjugate arises in physical or computation contexts and virtually never the transpose in isolation.
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