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Types of operators and matrices (Read 2132 times)
Gerrit-Jan Linker
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Types of operators and matrices
22.10.13 at 10:27:42
 
Types of operators and matrices
 
Matrices:
Xij=Xji : X is symmetric
Xij=-Xji : X is anti-symmetric
Xij=δijXii : X is diagonal
XX=1 : X is orthogonal
XX=XX : X is normal
 
Operators:
Ԇ= : is Hermitian
Ԇ=- : is anti-Hermitian
Ԇ=1 : is unitary
Ԇ=Ԇ : is normal
2= : is idempotent
 
The Hermitian conjugate or adjoint Ԇ of an operator is derfined as: <x|y>=<Ԇx|y>.
In matrix representation the adjoint or Hermitian conjugate of a matrix X is obtained by: (X)ij=X*ji
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« Last Edit: 22.10.13 at 10:34:09 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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