Section 23
Matrix decompositions
LU decomposition
avanzadoviz
Factors a matrix into triangular factors, with pivoting when needed.
QR decomposition
avanzadoviz
Q has orthonormal columns and R is upper triangular.
Spectral decomposition
avanzadoviz
Spectral form of real symmetric matrices.
SVD
avanzadoviz
Universal decomposition into singular directions and scales.
- data and image compression; - dimensionality reduction; - pseudoinverse and least squares; - recommender systems; - data analysis and machine learning.
Low-rank approximation
avanzadoviz
Approximates a matrix using its k dominant singular values.