Manuals/calci/QRDECOMPOSITION

QRDECOMPOSITION (Matrix)

• $Matrix$ is the set of values.

Description

• This function gives the value of QR Decomposition.
• In $QRDECOMPOSITION(Matrix)$,$Matrix$ 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 $A=QR$,where $Q$ stands for orthogonal matrix and $R$ stands for Upper Triangular matrix.
• An orthogonal matrix should satisfy $Q^{T}Q=I$,where $I$ is identity or Unitary matrix.
• $Q^{T}$ 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