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linalg::isHermitian

Checks whether a matrix is Hermitian

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Syntax

linalg::isHermitian(A)

Description

linalg::isHermitian(A) determines whether the matrix A is Hermitian, i.e., whether , where denotes the conjugate matrix.

If the component ring of the matrix A does not provide the method "conjugate", then A is tested for symmetry, i.e., linalg::isHermitian returns TRUE if and only if A satisfies the equation A = At.

Examples

Example 1

Here is an example of a Hermitian matrix:

A := Dom::Matrix(Dom::Complex)([[1, I], [-I, 1]])

linalg::isHermitian(A)

The following matrix is not Hermitian:

B := Dom::Matrix(Dom::Complex)([[1, -I], [-I, 1]])

linalg::isHermitian(B)

The reason is the following:

linalg::transpose(conjugate(B)) <> B

Example 2

Here is an example of a symmetric matrix over the integers:

C := Dom::Matrix(Dom::Integer)([[1, 2], [2, -1]])

linalg::isHermitian(C)

Parameters

A

A square matrix of a domain of category Cat::Matrix

Return Values

Either TRUE or FALSE.

See Also

MuPAD Functions

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