test if a Matrix is orthogonal - Maple Help

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Student[LinearAlgebra][IsOrthogonal] - test if a Matrix is orthogonal

Student[LinearAlgebra][IsUnitary] - test if a Matrix is unitary

Calling Sequence

IsOrthogonal(A, options)

IsUnitary(A, options)

Parameters

A

-

square Matrix

options

-

(optional) parameters; for a complete list, see LinearAlgebra[IsOrthogonal]

Description

• 

The IsOrthogonal(A) command determines if A is an orthogonal Matrix (A.A+=Id, where A+ is the transpose and Id is the identity Matrix).

  

In general, the IsOrthogonal command returns true if it can determine that Matrix A is orthogonal, false if it can determine that the Matrix is not orthogonal, and FAIL otherwise.

• 

The IsUnitary(A) command determines if A is a unitary Matrix (A.A*=Id, where A* is the Hermitian transpose and Id is the identity Matrix).

  

In general, the IsUnitary command returns true if it can determine that Matrix A is unitary, false if it can determine that the Matrix is not unitary, and FAIL otherwise.

Examples

withStudent[LinearAlgebra]:

G:=RotationMatrixπ7

G:=cos17πsin17πsin17πcos17π

(1)

IsOrthogonalG

true

(2)

mapsimplify,G.G%T

1001

(3)

Q:=10310,1010|10I10,310I10

Q:=31010110I1011010310I10

(4)

IsOrthogonalQ

false

(5)

IsUnitaryQ

true

(6)

See Also

LinearAlgebra[IsOrthogonal], map, simplify, Student[LinearAlgebra], Student[LinearAlgebra][IdentityMatrix], Student[LinearAlgebra][Operators], Student[LinearAlgebra][RotationMatrix]


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