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

=QRDECOMPOSITION(A1:B2)

 ``` -0.19611613513818393 -0.9805806756909202 ``` ```-0.9805806756909202 0.19611613513818393 ``` ```-10.19803902718557 13.5320133245347 ``` ```-1.1102230246251565e-15 -8.825226081218279 ```
A B C
1 3 8 -5
2 4 -6.3 9
3 2 5 -1

=QRDECOMPOSITION(A1:C3)

 ``` -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 ```

QR Decomposition