# Difference between revisions of "Manuals/calci/QRDECOMPOSITION"

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

A B
1 2 6
2 10 -15

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

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

2. QRDECOMPOSITION([[3,8,-5],[4,-6.3,9],[2,5,-1]])

 ``` -0.5570860145311556 0.631547425332445 -0.5392615524675877 ``` -0.7427813527082074 -0.669329688618384 -0.01654176541311622 -0.3713906763541037 0.3913382392381005 0.841975859527614 -5.385164807134504 -1.634118975958056 -3.528211425363985 ```-2.1551618871879059e-16 11.22584763714588 -9.573042563465782 ``` ```5.3446973501217775e-17 0 1.7054560140922779 ```