Manuals/calci/SVF

Revision as of 17:11, 26 July 2017 by Devika (talk | contribs)
SVF (Matrix)


  • is any set of values.

Description

  • This function shows the Singular value of a given matrix in descending order.
  • In  ,   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   where   is any square real or complex Unitary matrix of order  .
  •   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 Failed to parse (syntax error): {\displaystyle M^{∗}M}
.
*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 Failed to parse (syntax error): {\displaystyle M^∗M}
 and Failed to parse (syntax error): {\displaystyle MM^∗}
.