# Conjugate transpose of a matrix

## Hermitian matrix

In mathematics, the conjugate transpose or Hermitian transpose of an m-by-n matrix A {\displaystyle {\boldsymbol {A}}} {\boldsymbol {A}} with complex entries is .

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It enables operator overloading for classes. The result is a 2-by-4 matrix. B has the same elements as A , but the row and column index for each element are interchanged. When no complex elements are present, A' produces the same result as A. The result, B , contains the elements of A with the row and column indices interchanged.

In mathematics, a Hermitian matrix or self-adjoint matrix is a complex square matrix that is equal to its own conjugate transpose —that is, the element in the i -th row and j -th column is equal to the complex conjugate of the element in the j -th row and i -th column, for all indices i and j :. Hermitian matrices can be understood as the complex extension of real symmetric matrices. Hermitian matrices are named after Charles Hermite , who demonstrated in that matrices of this form share a property with real symmetric matrices of always having real eigenvalues. Hermitian matrices can be characterized in a number of equivalent ways, some of which are listed below:. This is also the way that the more general concept of self-adjoint operator is defined. Hermitian matrices are fundamental to the quantum theory of matrix mechanics created by Werner Heisenberg , Max Born , and Pascual Jordan in

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## transpose conjugate

Tool to calculate adjoint matrix or Hermitian transpose. The adjoint matrix is the transpose of the conjugate matrix of a matrix M.

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