Content deleted Content added
added alternate definition, format cleanup |
m →Generalizations: link fix |
||
Line 49:
==Generalizations==
The last property given above shows that if one views ''A'' as a [[linear map]] from the Euclidean [[Hilbert space]] '''C'''<sup>''n''</sup> to '''C'''<sup>''m''</sup>, then the matrix ''A''<sup>*</sup> corresponds to the [[Hermitian adjoint|adjoint operator]] of ''A''. The concept of adjoint operators between Hilbert spaces can thus be seen as a generalization of the conjugate transpose of matrices.
Another generalization is available: suppose ''A'' is a linear map from a complex [[vector space]] ''V'' to another ''W'', then the [[complex conjugate linear map]] as well as the [[transpose of a linear map|transposed linear map]] are defined, and we may thus take the conjugate transpose of ''A'' to be the complex conjugate of the transpose of ''A''. It maps the conjugate [[dual space|dual]] of ''W'' to the conjugate dual of ''V''.
| |||