Learn Linear Algebra

Getting started

This website is designed to help students build a strong foundation in linear algebra by providing guidance on essential proofs. This is meant for introductory topics including vectors, matrices, row operations on matrices, linear transformations, determinants, vector spaces, eigenvalues, orthogonality, and much more. Below, you'll find various sections that cover key topics for getting started.

Fundamental Concepts in Linear Algebra

Proofs related to the fundamental concepts in linear algebra, including row reductions, echelon forms, vector equations, matrix equations, solution sets of linear systems, and linear independence.

Matrices and Determinants

Proofs concerning matrices and determinants, covering matrix operations, properties of invertible matrices, matrix factorizations, and applications of Cramers rule.

Vector spaces, Eigenvalues, and eigenvectors

Proofs regarding vector spaces, subspaces, linear transformations, eigenvectors, and eigenvalues, including linear independence, bases, coordinate systems, dimensions, ranks, the characteristic equation, and diagonalization.

Orthogonality, Least Squares and Symmetric Matrices

Proofs related to orthogonality, least squares problems, and symmetric matrices, including the Gram-Schmidt process and the diagonalization of symmetric matrices.