Linear Algebra Guide

Linear algebra is a branch of mathematics that studies vectors, matrices, and linear transformations. It has applications in many fields, including physics, engineering, computer science, and economics. This guide will provide an overview of the key concepts and topics in linear algebra.

Key Concepts

Vectors: A vector is a mathematical object that has both magnitude and direction. In linear algebra, vectors are typically represented as columns or rows of numbers.
Matrices: A matrix is a rectangular array of numbers. Matrices are used to represent systems of linear equations and perform operations such as matrix multiplication and matrix inversion.
Linear Transformations: A linear transformation is a function that maps vectors from one vector space to another. Linear transformations are represented by matrices.

Topics

Vector Spaces: A vector space is a collection of vectors that can be added together and multiplied by scalars.
Basis and Dimension: A basis is a set of vectors that can be used to represent any vector in a vector space. The dimension of a vector space is the number of vectors in a basis.
Eigenvalues and Eigenvectors: Eigenvalues and eigenvectors are special values and vectors associated with a linear transformation. They are used to analyze the behavior of linear transformations.

Resources

For more in-depth information on linear algebra, you can check out our Linear Algebra Resources.