Manuals/calci/QRDECOMPOSITION

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QRDECOMPOSITION (Matrix)


  • is the set of values.

Description

  • This function gives the value of QR Decomposition.
  • In  ,  is any matrix.
  • QR Decomposition is also called QR Factorization.
  • QR Decomposition is defined by the product of Orthogonal matrix and Upper Triangular matrix.
  • Consider any square matrix A may be decomposed as  ,where   stands for orthogonal matrix and   stands for Upper Triangular matrix.
  • An orthogonal matrix should satisfy  ,where   is identity or Unitary matrix.
  •   is the transpose matrix of Q.
  • If the given matrix A is non singular, then this factorization is unique.
  • Gram-Schmidt process is one of the process of computing decomposition in QR Decomposition method.

Examples

1. QRDECOMPOSITION([[2,6],[10,-15]])

 -0.19611613513818393   -0.9805806756909202
-0.9805806756909202 0.19611613513818393
-10.19803902718557	13.5320133245347
-1.1102230246251565e-15 -8.825226081218279