MathCastle.org
0 XPSign up
← All courses

Linear Algebra

11 topics · study sheets, quizzes, and tests.

Start the course

Go through each topic step by step, with 10 timed practice problems after every section.

Start
Final Test (30) Big Test (50) Print the course (PDF)Suggest a problem

Topics

1.

Matrices & Systems

Arithmetic with grids of numbers

StudyQuizUnit Test
2.

Row Reduction & Rank

Gaussian elimination and the shape of solution sets

StudyQuizUnit Test
3.

Determinants & Inverses

One number that decides invertibility

StudyQuizUnit Test
4.

Vector Spaces & Bases

Span, independence, basis, dimension

StudyQuizUnit Test
5.

Linear Transformations

Kernel, image, rotations and reflections

StudyQuizUnit Test
6.

Orthogonality & Least Squares

Projections, distance, and best fit

StudyQuizUnit Test
7.

Eigenvalues

The directions a matrix merely stretches

StudyQuizUnit Test
8.

Diagonalization & Matrix Powers

A = PDP⁻¹ and everything it unlocks

StudyQuizUnit Test
9.

Symmetric Matrices & Quadratic Forms

The spectral theorem and definiteness

StudyQuizUnit Test
10.

Singular Values & the SVD

Every matrix is rank-one layers, sorted by importance

StudyQuizUnit Test
11.

Markov Chains & Long-Run Behavior

Steady states, mixing, and absorbing states

StudyQuizUnit Test