---
title: Matrix Computations
description: Matrix computations involve the algorithmic manipulation of matrices to solve scientific and engineering problems. Learners will understand matrix multiplication, inversion, and decomposition techniques optimized for speed and numerical accuracy on computers.
category: mathematics
subcategory: numerical-linear-algebra
difficulty: beginner, intermediate, advanced
url: /subject/matrix-computations
---

# Matrix Computations

Matrix computations involve the algorithmic manipulation of matrices to solve scientific and engineering problems. Learners will understand matrix multiplication, inversion, and decomposition techniques optimized for speed and numerical accuracy on computers.

## Available Resources

2 Books • 3 Websites

## Websites

### 1. Cleve's Corner (MATLAB)

Blog by Cleve Moler, creator of MATLAB and co-founder of MathWorks, covering numerical linear algebra, floating-point arithmetic, matrix algorithms, and the history of scientific computing through short MATLAB experiments. Readers gain intuition for how eigenvalue, SVD, and linear-solver routines behave in practice.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://blogs.mathworks.com/cleve/

**Tags:** numerical-linear-algebra, matlab, floating-point, scientific-computing

### 2. The Matrix Cookbook

Petersen and Pedersen's free reference compendium of matrix identities, derivatives, inverses, decompositions, and statistical results for multivariate Gaussians. Used as a lookup sheet when deriving gradients in machine learning, statistics, and signal processing rather than as a text for learning the underlying theory.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf

**Tags:** matrix-calculus, matrix-identities, linear-algebra, reference

### 3. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

## Books

### 1. Numerical Linear Algebra, Twenty-fifth Anniversary Edition

**Author:** Lloyd N. Trefethen, David Bau III

Forty short lectures on matrix computation: QR factorization, least squares, conditioning and backward error analysis, floating-point arithmetic, eigenvalue algorithms, and Krylov subspace iterations including GMRES and conjugate gradients. The 2022 reissue adds a foreword by Nagy and afterword by Nakatsukasa.

**Difficulty:** Advanced | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/1611977150?tag=edmonddante07-20

**Tags:** numerical-linear-algebra, matrix-factorization, eigenvalue-algorithms, krylov-subspace-methods, conditioning

### 2. Applied Numerical Linear Algebra

**Author:** James W. Demmel

Graduate textbook on the algorithms behind dense and sparse matrix computations: linear systems, least squares, eigenvalue and singular value problems, and iterative methods, with attention to error analysis and performance. Readers learn to choose, analyze, and implement stable numerical linear algebra routines.

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/9386235331?tag=edmonddante07-20

**Tags:** books, mathematics-statistics, numerical-linear-algebra

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