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Manuals/calci/QRDECOMPOSITION (view source)
Revision as of 10:48, 4 September 2017
, 10:48, 4 September 2017→Description
*QR Decomposition is also called QR Factorization.
*QR Decomposition is also called QR Factorization.
*QR Decomposition is defined by the product of Orthogonal matrix and Upper Triangular matrix.
*QR Decomposition is defined by the product of Orthogonal matrix and Upper Triangular matrix.
*Consider any square matrix A may be decomposed as <math>A=QR</math>,where <math>Q</math> stands for orthogonal matrix and <math>R</math> stands for Upper Triangular matrix.
*Consider any square matrix A may be decomposed as <math>A=QR</math>, where <math>Q</math> stands for orthogonal matrix and <math>R</math> stands for Upper Triangular matrix.
*An orthogonal matrix should satisfy <math>Q^TQ=I</math>,where <math>I</math> is identity or Unitary matrix.
*An orthogonal matrix should satisfy <math>Q^TQ=I</math>, where <math>I</math> is identity or Unitary matrix.
*<math>Q^T</math> is the transpose matrix of Q.
*<math>Q^T</math> is the transpose matrix of Q.
*If the given matrix A is non singular, then this factorization is unique.
*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.
*Gram-Schmidt process is one of the process of computing decomposition in QR Decomposition method.