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In mathematics, the conjugate transpose, also known as the Hermitian transpose, of an complex matrix is an matrix obtained by transposing and applying complex conjugation to each entry (the complex conjugate of + being , for real numbers and ).
The complex conjugate transpose of a matrix interchanges the row and column index for each element, reflecting the elements across the main diagonal. The operation also negates the imaginary part of any complex numbers. For example, if B = A' and A(1,2) is 1+1i, then the element B(2,1) is 1-1i.
The complex conjugate transpose of a matrix interchanges the row and column index for each element, reflecting the elements across the main diagonal. The operation also negates the imaginary part of any complex numbers.
7 lis 2024 · In linear algebra, it is common to apply both the complex conjugate and transpose to the same matrix. The matrix obtained from a given matrix by this combined operation is commonly called the conjugate transpose of .
3 sty 2024 · A matrix \(A = \left[ a_{ij} \right]\) is called a complex matrix if every entry \(a_{ij}\) is a complex number. The notion of conjugation for complex numbers extends to matrices as follows: Define the conjugate of \(A = \left[ a_{ij} \right]\) to be the matrix
7 lis 2024 · The conjugate transpose of an m×n matrix A is the n×m matrix defined by A^ (H)=A^_^ (T), (1) 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)=A^_^ (T)=A^ (T)^_.
Conjugate-transpose the first two levels of a rank-3 array, effectively treating it as a matrix of vectors:
