Conjugate transpose: Difference between revisions
Realize in F#
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}</lang>
=={{header|F_Sharp|F#}}==
<lang fsharp>
// Conjugate transpose. Nigel Galloway: January 10th., 2022
let fN g=let g=g|>List.map(List.map(fun(n,g)->System.Numerics.Complex(n,g)))|>MathNet.Numerics.LinearAlgebra.MatrixExtensions.matrix in (g,g.ConjugateTranspose())
let fG n g=(MathNet.Numerics.LinearAlgebra.Matrix.inverse n-g)|>MathNet.Numerics.LinearAlgebra.Matrix.forall(fun(n:System.Numerics.Complex)->abs n.Real<1e-14&&abs n.Imaginary<1e-14)
let test=[fN [[(3.0,0.0);(2.0,1.0)];[(2.0,-1.0);(1.0,0.0)]];fN [[(1.0,0.0);(1.0,0.0);(0.0,0.0)];[(0.0,0.0);(1.0,0.0);(1.0,0.0)];[(1.0,0.0);(0.0,0.0);(1.0,0.0)]];fN [[(1.0/sqrt 2.0,0.0);(1.0/sqrt 2.0,0.0);(0.0,0.0)];[(0.0,1.0/sqrt 2.0);(0.0,-1.0/sqrt 2.0);(0.0,0.0)];[(0.0,0.0);(0.0,0.0);(0.0,1.0)]]]
test|>List.iter(fun(n,g)->printfn $"Matrix\n------\n%A{n}\nConjugate transposed\n--------------------\n%A{g}\nIs hermitian: %A{n.IsHermitian()}\nIs normal: %A{n*g=g*n}\nIs unitary: %A{fG n g}\n")
</lang>
{{out}}
<pre>
Matrix
------
DenseMatrix 2x2-Complex
(3, 0) (2, 1)
(2, -1) (1, 0)
Conjugate transposed
--------------------
DenseMatrix 2x2-Complex
(3, -0) (2, 1)
(2, -1) (1, -0)
Is hermitian: true
Is normal: true
Is unitary: false
Matrix
------
DenseMatrix 3x3-Complex
(1, 0) (1, 0) (0, 0)
(0, 0) (1, 0) (1, 0)
(1, 0) (0, 0) (1, 0)
Conjugate transposed
--------------------
DenseMatrix 3x3-Complex
(1, -0) (0, -0) (1, -0)
(1, -0) (1, -0) (0, -0)
(0, -0) (1, -0) (1, -0)
Is hermitian: false
Is normal: true
Is unitary: false
Matrix
------
DenseMatrix 3x3-Complex
(0.707107, 0) (0.707107, 0) (0, 0)
(0, 0.707107) (0, -0.707107) (0, 0)
(0, 0) (0, 0) (0, 1)
Conjugate transposed
--------------------
DenseMatrix 3x3-Complex
(0.707107, -0) (0, -0.707107) (0, -0)
(0.707107, -0) (0, 0.707107) (0, -0)
(0, -0) (0, -0) (0, -1)
Is hermitian: false
Is normal: true
Is unitary: true
</pre>
=={{header|Factor}}==
Before the fix to [https://github.com/slavapestov/factor/issues/484 Factor bug #484], <code>m.</code> gave the wrong answer and this code failed. Factor 0.94 is too old to work.
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