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Manuals/calci/QRDECOMPOSITION (view source)
Revision as of 21:40, 12 July 2017
, 21:40, 12 July 2017Created page with "<div style="font-size:30px">'''QRDECOMPOSITION (Matrix) '''</div><br/> *<math>Matrix</math> is the set of values. ==Description== *This function gives the value of QR Decompo..."
<div style="font-size:30px">'''QRDECOMPOSITION (Matrix) '''</div><br/>
*<math>Matrix</math> is the set of values.
==Description==
*This function gives the value of QR Decomposition.
*In <math>QRDECOMPOSITION (Matrix)</math>,<math>Matrix</math> 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 <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.
*<math>Q^T</math> 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]])
{| border="1" cellpadding="5" cellspacing="0"
|-
|
-0.19611613513818393 -0.9805806756909202
|| -0.9805806756909202 0.19611613513818393
|-
|
-10.19803902718557 13.5320133245347
||-1.1102230246251565e-15 -8.825226081218279
|}
*<math>Matrix</math> is the set of values.
==Description==
*This function gives the value of QR Decomposition.
*In <math>QRDECOMPOSITION (Matrix)</math>,<math>Matrix</math> 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 <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.
*<math>Q^T</math> 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]])
{| border="1" cellpadding="5" cellspacing="0"
|-
|
-0.19611613513818393 -0.9805806756909202
|| -0.9805806756909202 0.19611613513818393
|-
|
-10.19803902718557 13.5320133245347
||-1.1102230246251565e-15 -8.825226081218279
|}