Matrix Decompositions
LU, QR, Cholesky, SVD, and eigen-decompositions and their computational properties.
Matrix Decompositions. LU, QR, Cholesky, SVD, and eigen-decompositions and their computational properties. This page collects canonical references that organise the subject and provide entry points to its main techniques.
Foundations and canonical references
The standard treatments of matrix decompositions approach the subject from complementary angles. Golub, Matrix Computations (2013) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Trefethen, Numerical Linear Algebra (1997) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for matrix decompositions include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2013Matrix Computationsgolub-2013, vanloan-2013
- textbook · primary · 1997Numerical Linear Algebratrefethen-1997, bau-1997
In context
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