nLab QR decomposition

Idea

In linear algebra, the decomposition of a matrix $M$ as the matrix product $M = Q R$ of

• an orthonormal matrix $Q$

and

• an upper triangular matrix $R$

is is called QR decomposition or QR factorization.

Properties

Computation

QR decompositions may be computed via

• the Gram-Schmidt process

• …

Related concepts

• matrix decomposition

  • Gauss decomposition

  • polar decomposition

  • LU decomposition

• Iwasawa decomposition

Literature

• Wikipedia, QR decomposition

Relation of QR decompositions (and some other matrix decompositions) to flows of integrable systems:

• P. Deift, L. C. Li, C.Tomei, Matrix factorizations and integrable systems, Commun. Pure Appl. Math. 42 4 (1989) 443-521 [doi:10.1002/cpa.3160420405]