Linear Algebra

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Chapter Overview

Linear Algebra

Linear algebra is a branch of mathematics that deals with vectors, vector spaces, and linear transformations. It is a fundamental tool in engineering and science, providing the mathematical framework for solving systems of linear equations, performing data analysis, and modeling complex phenomena. In SepalSolver, we implement various linear algebra techniques to equip engineers with powerful tools for numerical computation and problem-solving.

Linear algebra techniques are widely used in applications such as computer graphics, machine learning, and structural analysis. They help in optimizing designs, analyzing data, and simulating physical systems.

In this chapter, we will explore different linear algebra methods, their implementations in SepalSolver, and practical examples demonstrating their applications.

Sections in this chapter

  1. 05.1Vectors and Matrices7 units · 7 examples · 14 min
  2. 05.2Matrix Slicing11 units · 8 examples · 20 min
  3. 05.3Matrix Vectors Operations Null Spaces5 units · 9 examples · 27 min
  4. 05.4LU Facorization and FactorUpdate5 units · 2 examples · 7 min
  5. 05.5Solution of Linear Systems4 units · 4 examples · 11 min
  6. 05.6Cholesky Factorization FactorUpdate Positive Definicy2 units · 2 examples · 7 min
  7. 05.7Generalized Cholesky Factorization and FactorUpdateNot yet written in the book
  8. 05.8Singular Value Decomposition1 examples · 5 min
  9. 05.9Sparse Matrices4 units · 13 examples · 30 min
  10. 05.10Solution Of Sparse Linear SystemNot yet written in the book
  11. 05.11Exercise On Linear AlgebraNot yet written in the book
Start: Vectors and Matrices