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Conjugate transpose: Difference between revisions
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* MathWorld: [http://mathworld.wolfram.com/ConjugateTranspose.html conjugate transpose], [http://mathworld.wolfram.com/HermitianMatrix.html Hermitian matrix], [http://mathworld.wolfram.com/NormalMatrix.html normal matrix], [http://mathworld.wolfram.com/UnitaryMatrix.html unitary matrix]
=={{header|Ada}}==
<lang Ada>with Ada.Text_IO; use Ada.Text_IO;
with Ada.Complex_Text_IO; use Ada.Complex_Text_IO;
with Ada.Numerics.Complex_Types; use Ada.Numerics.Complex_Types;
with Ada.Numerics.Complex_Arrays; use Ada.Numerics.Complex_Arrays;
procedure ConTrans is
subtype CM is Complex_Matrix;
S2O2 : constant Float := 0.7071067811865;
procedure Print (mat : CM) is begin
for row in mat'Range(1) loop for col in mat'Range(2) loop
Put(mat(row,col), Exp=>0, Aft=>4);
end loop; New_Line; end loop;
end Print;
function almostzero(mat : CM; tol : Float) return Boolean is begin
for row in mat'Range(1) loop for col in mat'Range(2) loop
if abs(mat(row,col)) > tol then return False; end if;
end loop; end loop;
return True;
end almostzero;
procedure Examine (mat : CM) is
CT : CM := Conjugate (Transpose(mat));
isherm, isnorm, isunit : Boolean;
begin
isherm := almostzero(mat-CT, 1.0e-6);
isnorm := almostzero(mat*CT-CT*mat, 1.0e-6);
isunit := almostzero(CT-Inverse(mat), 1.0e-6);
Print(mat);
Put_Line("Conjugate transpose:"); Print(CT);
Put_Line("Hermitian?: " & isherm'Img);
Put_Line("Normal?: " & isnorm'Img);
Put_Line("Unitary?: " & isunit'Img);
end Examine;
hmat : CM := ((3.0+0.0*i, 2.0+1.0*i), (2.0-1.0*i, 1.0+0.0*i));
nmat : CM := ((1.0+0.0*i, 1.0+0.0*i, 0.0+0.0*i),
(0.0+0.0*i, 1.0+0.0*i, 1.0+0.0*i),
(1.0+0.0*i, 0.0+0.0*i, 1.0+0.0*i));
umat : CM := ((S2O2+0.0*i, S2O2+0.0*i, 0.0+0.0*i),
(0.0+S2O2*i, 0.0-S2O2*i, 0.0+0.0*i),
(0.0+0.0*i, 0.0+0.0*i, 0.0+1.0*i));
begin
Put_Line("hmat:"); Examine(hmat); New_Line;
Put_Line("nmat:"); Examine(nmat); New_Line;
Put_Line("umat:"); Examine(umat);
end ConTrans;</lang>
{{out}}
<pre>hmat:
( 3.0000, 0.0000)( 2.0000, 1.0000)
( 2.0000,-1.0000)( 1.0000, 0.0000)
Conjugate transpose:
( 3.0000,-0.0000)( 2.0000, 1.0000)
( 2.0000,-1.0000)( 1.0000,-0.0000)
Hermitian?: TRUE
Normal?: TRUE
Unitary?: FALSE
nmat:
( 1.0000, 0.0000)( 1.0000, 0.0000)( 0.0000, 0.0000)
( 0.0000, 0.0000)( 1.0000, 0.0000)( 1.0000, 0.0000)
( 1.0000, 0.0000)( 0.0000, 0.0000)( 1.0000, 0.0000)
Conjugate transpose:
( 1.0000,-0.0000)( 0.0000,-0.0000)( 1.0000,-0.0000)
( 1.0000,-0.0000)( 1.0000,-0.0000)( 0.0000,-0.0000)
( 0.0000,-0.0000)( 1.0000,-0.0000)( 1.0000,-0.0000)
Hermitian?: FALSE
Normal?: TRUE
Unitary?: FALSE
umat:
( 0.7071, 0.0000)( 0.7071, 0.0000)( 0.0000, 0.0000)
( 0.0000, 0.7071)( 0.0000,-0.7071)( 0.0000, 0.0000)
( 0.0000, 0.0000)( 0.0000, 0.0000)( 0.0000, 1.0000)
Conjugate transpose:
( 0.7071,-0.0000)( 0.0000,-0.7071)( 0.0000,-0.0000)
( 0.7071,-0.0000)( 0.0000, 0.7071)( 0.0000,-0.0000)
( 0.0000,-0.0000)( 0.0000,-0.0000)( 0.0000,-1.0000)
Hermitian?: FALSE
Normal?: TRUE
Unitary?: TRUE</pre>
=={{header|Factor}}==
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