Randomized Linear Algebra

Randomized Linear Algebra. Sketching, randomized SVD, and probabilistic algorithms for large matrices. The literature on randomized linear algebra divides naturally along several axes: the foundational structures that organise the subject, the techniques that drive proofs and computations, the questions about classification or representation that animate current research, and the bridges to neighbouring areas of mathematics and science. The references below trace those axes through the canonical textbook treatments and recent technical contributions.

Foundations and canonical references

The standard treatments of randomized linear algebra approach the subject from complementary angles. Drineas, Lectures on Randomized Numerical Linear Algebra (2018) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques.

Recent technical contributions

A handful of recent papers carry the methodological frontier of randomized linear algebra forward. Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions (Halko et al., 2011) is a primary reference for this area and develops new techniques or results that downstream work builds on. Randomized numerical linear algebra: Foundations and algorithms (Martinsson et al., 2020) pushes the technical state of the art and is widely cited in subsequent work on the topic.

Open methodological questions for randomized linear algebra 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.