Theory and applications · Undergraduate course resource
Applied
Linear Algebra
Explore the geometry and applications of vectors, matrices, linear transformations, and least squares.
The course
About This Course
Study the theory and applications of linear algebra through worked examples. Topics include systems of linear equations, vector and matrix operations, linear transformations, determinants, vector spaces, bases and dimensions, eigenvalues and eigenvectors, orthogonality, projections, QR factorization, and least squares.
The learning path
From linear equations
to geometric insight.
Follow the original course sequence across eight recorded collections. Five collections are public; three require your existing membership.
Equations and Matrices
1 recorded collection
02Vectors
1 recorded collection
03Linear Transformations
1 recorded collection
04Matrices
1 recorded collection
05Vector Spaces
1 recorded collection
06Eigenvalues and Eigenvectors
1 recorded collection
07Orthogonality and Least Squares Part 1
1 recorded collection
08Orthogonality and Least Squares Part 2
1 recorded collection
The Algebra lecture library
Find your next lecture.
Search for a topic or choose a unit. Each collection includes worked examples, lecture descriptions, and a guided video player.
Course unit
Equations and Matrices
Equations and Matrices
Equations and Matrices
Solve systems of equations with row operations, augmented matrices, and reduced row echelon form.
Course unit
Vectors
Vectors
Vectors
Compute with vectors, linear combinations, spans, and linear independence.
Course unit
Linear Transformations
Linear Transformations
Linear Transformations
Represent linear transformations with matrices and explore rotations, reflections, one-to-one maps, and onto maps.
Course unit
Matrices
Matrices
Matrices
Multiply and invert matrices, compute determinants, and apply Cramer’s rule.
Course unit
Vector Spaces
Vector Spaces
Vector Spaces
Study subspaces, bases, dimensions, null spaces, row spaces, and coordinate systems.
Course unit
Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
Find eigenvalues and eigenvectors, diagonalize matrices, and compute matrix powers.
Course unit
Orthogonality and Least Squares Part 1
Orthogonality and Least Squares Part 1
Orthogonality and Least Squares Part 1
Build intuition for inner products, norms, orthogonality, and projections.
Course unit
Orthogonality and Least Squares Part 2
Orthogonality and Least Squares Part 2
Orthogonality and Least Squares Part 2
Use orthonormal bases, Gram–Schmidt, QR factorization, and least-squares approximations.
Members · Original example files
Put the ideas
into practice.
Browse the original worked-example PDFs, organized by topic, in the members-only archive.
Browse algebra example files ↗