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

Spreadsheet

	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

See Also

• LUDECOMPOSITION
• CHOLESKYFACTORIZATION
• CONFERENCE

References

• LU Decomposition

• List of Main Z Functions

• Z3 home