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Unitary matrix & Unit matrix (Read 3068 times)
Gerrit-Jan Linker
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Unitary matrix & Unit matrix
13.01.08 at 17:13:58
 
Unitary matrix
 
A is a unitary matrix if the adjoint of matrix A is equal to the inverse of A:
A = A-1
 
For an inverse matrix A the following relation is true:
AA-1 = A-1A = 1
 
It is therefore also true that:
AA = AA = 1
 
If A is a real and unitary matrix, then A is said to be orthogonal since AT = A-1
The adjoint of a matrix is the transpose and complex-conjugate of that matrix. If A is real the complex-conjugate is equal to itself so the adjoint is just the transpose of the matrix.
 
The unitary matrix is not to be confused with a unit matrix. For a unit matrix A it holds that 1A = A1 = A and (1)ij = δij
 
Examples of unit matrixes are:
10
01
 
 
100
010
001

 
See also:
The adjoint of a matrix
http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1200234640
Inverse of a matrix
http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1200240564
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« Last Edit: 26.01.08 at 22:45:35 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
Linker IT Software
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