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linalg::isUnitary -- test whether a matrix is unitary

Introduction

linalg::isUnitary tests whether the matrix A is a unitary matrix. An n x n matrix A is unitary, if A * transpose(conjugate(A)) = I, where I is the n x n identity matrix.

Call(s)

linalg::isUnitary(A)

Parameters

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

Returns

either TRUE, FALSE, or UNKNOWN.

Related Functions

linalg::orthog, linalg::scalarProduct

Details

Example 1

The following matrix is unitary:

>> A := 1/sqrt(5) * matrix([[1, 2], [2, -1]])
                           +-                -+
                           |    1/2      1/2  |
                           |   5      2 5     |
                           |   ----,  ------  |
                           |    5       5     |
                           |                  |
                           |     1/2     1/2  |
                           |  2 5       5     |
                           |  ------, - ----  |
                           |    5        5    |
                           +-                -+
>> linalg::isUnitary(A)
                                   TRUE

Changes




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