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linalg::isHermitean -- checks whether a matrix is Hermitean

Introduction

linalg::isHermitean(A) determines whether the matrix A is Hermitean, i.e., whether A=transpose(conjugate(A)).

Call(s)

linalg::isHermitean(A)

Parameters

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

Returns

either TRUE or FALSE.

Related Functions

linalg::isPosDef

Details

Example 1

Here is an example of a Hermitean matrix:

>> A := Dom::Matrix(Dom::Complex)([[1, I], [-I, 1]])
                               +-        -+
                               |   1,  I  |
                               |          |
                               |  - I, 1  |
                               +-        -+
>> linalg::isHermitean(A)
                                   TRUE

The following matrix is not Hermitean:

>> B := Dom::Matrix(Dom::Complex)([[1, -I], [-I, 1]])
                              +-          -+
                              |   1,  - I  |
                              |            |
                              |  - I,  1   |
                              +-          -+
>> linalg::isHermitean(B)
                                   FALSE

The reason is the following:

>> linalg::transpose(conjugate(B)) <> B
                       +-      -+    +-          -+
                       |  1, I  |    |   1,  - I  |
                       |        | <> |            |
                       |  I, 1  |    |  - I,  1   |
                       +-      -+    +-          -+

Example 2

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

>> C := Dom::Matrix(Dom::Integer)([[1, 2], [2, -1]])
                                +-       -+
                                |  1,  2  |
                                |         |
                                |  2, -1  |
                                +-       -+
>> linalg::isHermitean(C)
                                   TRUE

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