AI engineering glossary · Linear algebra
What is QR decomposition?
QR decomposition (also called QR factorisation): A factorisation of a matrix into an orthogonal matrix Q and an upper triangular matrix R. It is numerically stable and is used to solve least-squares problems and to compute eigenvalues.
QR decomposition: an example
For a tall 100 x 3 data matrix X, X = Q R with Q having 3 orthonormal columns; regression coefficients solve R b = Q^T y.
Related terms
More Linear algebra terms
- Quadratic form
- Rank
- Rank-nullity theorem
- Rank-one matrix
- Reduced row echelon form
- Rotation matrix
- Row echelon form
- Row space
Where you learn it
QR decomposition is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.