# 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