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In mathematics, the conjugate transpose or Hermitian transpose of an ''m''-by-''n'' matrix ' with complex entries is the ''n''-by-''m'' matrix ' * obtained from ' by taking the transpose and then taking the complex conjugate of each entry (i.e., negating their imaginary parts but not their real parts). The conjugate transpose is formally defined by : where the subscripts denote the ''i'',''j''-th entry, for 1 ≤ ''i'' ≤ ''n'' and 1 ≤ ''j'' ≤ ''m'', and the overbar denotes a scalar complex conjugate. (The complex conjugate of , where ''a'' and ''b'' are reals, is .) This definition can also be written as : where denotes the transpose and or , commonly used in linear algebra * (sometimes pronounced as "' dagger"), universally used in quantum mechanics * , although this symbol is more commonly used for the Moore–Penrose pseudoinverse In some contexts, denotes the matrix with complex conjugated entries, and the conjugate transpose is then denoted by . ==Example== If : then : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「conjugate transpose」の詳細全文を読む スポンサード リンク
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