Welcome to the introduction to linear algebra by Gilbert Strang. This book is a comprehensive guide to the fundamental concepts of linear algebra, a branch of mathematics that deals with vectors, matrices, and linear transformations.
Key Concepts
- Vectors: Represented by arrows, vectors are used to describe quantities that have both magnitude and direction.
- Matrices: A rectangular array of numbers, matrices are used to represent systems of linear equations and transformations.
- Linear Transformations: Functions that preserve linear combinations of vectors.
Why Study Linear Algebra?
Linear algebra is a fundamental tool in many fields, including physics, engineering, computer science, and economics. It is used to solve problems involving systems of equations, find eigenvalues and eigenvectors, and analyze data.
Book Overview
This book covers a wide range of topics, including:
- Vector Spaces: Introduction to vector spaces, linear combinations, and bases.
- Matrices: Operations on matrices, determinants, and eigenvalues.
- Systems of Linear Equations: Methods for solving systems of linear equations, including Gaussian elimination and matrix factorization.
- Linear Transformations: Definition and properties of linear transformations, and their representation by matrices.
Additional Resources
For further reading, you may want to explore our Linear Algebra Tutorials.
Vector Space
Matrix
Linear_Transformation