Manuals/calci/SVF - Revision history

Devika: /* Related Videos */

2019-04-25T18:05:34Z

Devika: /* Examples */

2019-04-25T18:04:58Z

Examples

Devika at 22:30, 26 July 2017

2017-07-26T22:30:54Z

Devika: /* Description */

2017-07-26T22:14:24Z

Description

Devika at 22:11, 26 July 2017

2017-07-26T22:11:47Z

Devika: Created page with "
'''SVF (Matrix)'''

* $Matrix$ is any set of values. ==Description== *This function shows the Singular value of a given matri..."

2017-07-26T22:06:07Z

Created page with "<div style="font-size:30px">'''SVF (Matrix)'''</div><br/> *<math>Matrix</math> is any set of values. ==Description== *This function shows the Singular value of a given matri..."

New page

<div style="font-size:30px">'''SVF (Matrix)'''</div><br/>
*<math>Matrix</math> is any set of values.

==Description==
*This function shows the Singular value of a given matrix in descending order.
*In <math>SVF(Matrix)</math>, <math>Matrix</math> is any matrix with array of values.
*Singular value decomposition is defined by the factorization of a real or complex matrix.
*It is the generalization of the Eigen decomposition of a symmetric matrix with positive eigen values to any mxn matrix through an extension of the polar decomposition.
*Singular value decomposition is of the form <math>U \Sigma V</math> where <math> U</math> is any square real or complex Unitary matrix of order <math>mxm</math>.
*<math>\Sigma </math> is a mxn rectangular diagonal matrix with non negative real numbers.
*V is also any square real or complex Unitary matrix of order nxn.
*The columns of U and V are called left Singular and right Singular vectors of the matrix.
*To find Singular Value Decomposition we have to follow the below rules:
*The left-singular vectors of the matrix M are a set of orthonormal eigenvectors of MM∗.
*The right-singular vectors of M are a set of orthonormal eigenvectors of <math>M^∗M</math>.
*The non-zero singular values of M (found on the diagonal entries of Σ) are the square roots of the non-zero eigenvalues of both <math>M^∗M</math> and <math>MM^∗</math>.

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 ==Related Videos==
-{{#ev:youtube|v=4g-zS32oKEw|280|center|}}
+{{#ev:youtube|v=4g-zS32oKEw|280|center|Singular Values}}
 ==See Also==

← Older revision		Revision as of 18:04, 25 April 2019
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	==Examples==		==Examples==
		+
		+	==Related Videos==
		+
		+	{{#ev:youtube\|v=4g-zS32oKEw\|280\|center\|}}

	==See Also==		==See Also==

← Older revision		Revision as of 22:30, 26 July 2017
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	The right-singular vectors of M are a set of orthonormal eigenvectors of <math>M^M</math>.		The right-singular vectors of M are a set of orthonormal eigenvectors of <math>M^M</math>.
	The non-zero singular values of M (found on the diagonal entries of Σ) are the square roots of the non-zero eigenvalues of both <math>M^M</math> and <math>MM^*</math>.		The non-zero singular values of M (found on the diagonal entries of Σ) are the square roots of the non-zero eigenvalues of both <math>M^M</math> and <math>MM^*</math>.
		+
		+	==Examples==
		+
		+	==See Also==
		+	*[[Manuals/calci/LUDECOMPOSITION \| LUDECOMPOSITION ]]
		+	*[[Manuals/calci/CHOLESKYFACTORIZATION \| CHOLESKYFACTORIZATION ]]
		+	*[[Manuals/calci/QRDECOMPOSITION \| QRDECOMPOSITION ]]
		+
		+	==References==
		+	*[https://en.wikipedia.org/wiki/Singular_value_decomposition Decomposition]
		+
		+
		+	*[[Z_API_Functions \| List of Main Z Functions]]
		+
		+	*[[ Z3 \| Z3 home ]]

@@ Line 13: / Line 13: @@
 *To find Singular Value Decomposition we have to follow the below rules:
   *The left-singular vectors of the matrix M are a set of orthonormal eigenvectors of MM∗.
-  *The right-singular vectors of M are a set of orthonormal eigenvectors of <math>M^{∗}M</math>.
+  *The right-singular vectors of M are a set of orthonormal eigenvectors of <math>M^*M</math>.
-  *The non-zero singular values of M (found on the diagonal entries of Σ) are the square roots of the non-zero eigenvalues of both <math>M^∗M</math> and <math>MM^∗</math>.
+  *The non-zero singular values of M (found on the diagonal entries of Σ) are the square roots of the non-zero eigenvalues of both <math>M^*M</math> and <math>MM^*</math>.