Matrix transformations

Matrix decomposition can be used in the following cases:

  • as an intermediate step when solving systems of linear equations
  • for matrix inversion
  • when calculating determinants
  • when finding eigenvalues and eigenvectors of a matrix
  • when computing analytic functions of matrices
  • when using the least squares method
  • in the numerical solution of differential equations

Different matrix decomposition types are used depending on the problem.

Function

Action

Cholesky

Computes the Cholesky decomposition

Eig

Computes the eigenvalues and right eigenvectors of a square matrix

EigVals

Computes the eigenvalues of a general matrix

LU

LU factorization of a matrix as the product of a lower triangular matrix and an upper triangular matrix

LUP

LUP factorization with partial pivoting, which refers to LU decomposition with row permutations only: PA=LU

QR

Compute the qr factorization of a matrix

SVD

Singular Value Decomposition