Difference between revisions of "Manuals/calci/HADAMARD"

Revision as of 09:24, 24 April 2015

MATRIX("HADAMARD",order)

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

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

So the possible order of the matrix is 1,2 or positive multiple of 4.
The few examples of hadamard matrices are:
$H_{1}={\begin{bmatrix}1\\\end{bmatrix}}*H_{2}={\begin{bmatrix}1&1\\1&-1\\\end{bmatrix}}*H_{3}={\begin{bmatrix}1&1&1&1\\1&-1&1&-1\\1&1&-1&-1\\1&-1&-1&1\\\end{bmatrix}}$

@@ Line 5: / Line 5: @@
 *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.
+*Also the rows of that matrix are orthogonal.
+*So H be a Hadamard matrix of order 2n.
 *The transpose of H is closely related to its inverse.
 *The equivalent definition for hadamard matrix is:
@@ Line 11: / Line 12: @@
 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:
+*The few examples of hadamard matrices are:
+*<math>H_1=\begin{bmatrix}
+\\
+\end{bmatrix}
+*H_2 = \begin{bmatrix}
+  & 1 \\
+  & -1 \\
+\end{bmatrix}
+*H_3 =\begin{bmatrix}
+  & 1 & 1 & 1 \\
+  & -1 & 1 & -1\\
+& 1 & -1 & -1 \\
+& -1 & -1 & 1\\
+\end{bmatrix}</math>