# Randomised linear algebra See random matrices, vector random projections and many other related tricks Notes on doing linear algebra operations using randomised matrix projections. Useful for, e.g. randomised regression.

## Context

Obligatory Igor Carron mention: Random matrices are too damn large. Martinsson (2016) seems to be a fresh review of the action.

## Randomisation in matrix factorization

See various matrix factorisation methods.

## Hutchinson trace estimator

Shakir Mohamed mentions Hutchinson’s Trick, and was introduced to it, as I was, by Dr Maurizio Filippone. This trick also works with efficiently with the ensemble Kalman filter, where the randomised products are cheap.

Overview — imate Manual

## Tools

### imate

Overview — imate

The main purpose of ımate is to estimate the algebraic quantity $\operatorname{trace}(f(\mathbf{A}))$ where $$\mathbf{A}$$ is a square matrix, $$f$$ is a matrix function, and trace $$(\cdot)$$ is the trace operator. Imate can also compute variants of $$(1)$$, such as $\operatorname{trace}(\mathbf{B} f(\mathbf{A}))$ and $\operatorname{trace}(\mathbf{B} f(\mathbf{A}) \mathbf{C} f(\mathbf{A}))$ where $$\mathbf{B}$$ and $$\mathbf{C}$$ are matrices. Other variations include the cases where $$\mathbf{A}$$ is replaced by $$\mathbf{A}^{\top} \mathbf{A}$$ in the above expressions.

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