Difference between revisions of "Manuals/calci/HADAMARD"

Revision as of 13:29, 23 April 2015

MATRIX("HADAMARD",order)

This function gives the matrix satisfying the property of Hadamard.
A Hadamard matrix is the square matrix with the entries of 1 and -1.
Also the rows of that matrix are orthogonal.Let H be a Hadamard matrix of order n.
The transpose of H is closely related to its inverse.
The equivalent definition for hadamard matrix is:

 $HH^{T}=nI_{n}$

where $I_{n}$ is the n × n identity matrix and $H^{T}$ is the transpose of H.

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-<div style="font-size:30px">'''HADAMARD'''</div><br/>
+<div style="font-size:30px">'''MATRIX("HADAMARD",order)'''</div><br/>
+*<math>order</math> is the order of the hadamard matrix.
+==Description==
+*This function gives the matrix satisfying the property of Hadamard.
+*A Hadamard matrix is the square matrix with the entries of 1 and -1.
+*Also the rows of that matrix are orthogonal.Let H be a Hadamard matrix of order n.
+*The transpose of H is closely related to its inverse.
+*The equivalent definition for hadamard matrix is:
+ <math>H H^{T} = n I_{n}</math>
+where <math>I_{n}</math> is the n × n identity matrix and <math>H^T</math> is the transpose of H.
+*So the possible order of the matrix is 1,2 or positive multiple of 4.
+*The examples of hadamard matrices are: