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Linear Algebra for Computing: Vectors, Matrices, Systems, Determinants, Eigenvalues

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11 pages 2026
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Preview generated from this document’s own text

This study guide covers core linear algebra for computing, IT, mathematics and engineering students, from vector and matrix operations through systems, determinants, inverses, transformations and eigenvalues. It combines definitions, rules, step-by-step worked examples, computing applications, a summary table and practice questions with answers for exam preparation.

  • Vector operations, norms, angles, projections and cross products
  • Matrix notation, products, transposes and common matrix operations
  • Linear systems, Gaussian elimination, determinants, inverses and Cramer's rule
  • Linear independence, span, basis, rank and linear transformations
  • 2D computer graphics transformations and eigenvalue/eigenvector problems
  • Markov chains, least-squares fitting, orthogonalisation, summary notes and practice questions
VectorsMatricesGaussian eliminationDeterminants and inversesLinear transformationsEigenvalues and eigenvectorsLeast squaresComputer graphics

Frequently asked questions

Who is this guide for?

It is designed for students taking a first linear algebra course in computing, IT, mathematics or engineering.

Does the document include worked examples?

Yes. Each major section introduces the relevant definitions and rules before presenting worked examples in an exam-oriented format.

Does it cover applications of linear algebra?

Yes. Applications include 2D graphics transformations, Markov chains, least-squares fitting, orthogonalisation and computing-focused examples.

Are practice materials included?

Yes. The guide ends with a summary table and practice questions with answers for review and exam preparation.

Does it cover both introductory and intermediate topics?

It covers the main topics of a typical first course, progressing from basic vector and matrix operations to rank, transformations, eigenvalues and applied methods.

Document details

Pages
11
Words
3,678
Format
PDF
Language
English
Uploaded
Nov 2026
Updated
Nov 2026
Type
Study guide
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