“Know how to solve every problem that has been solved.” “What I cannot create, I do not understand.” — Richard Feynman

Linear Algebra

Courses

Vectors, matrices, eigenproblems — the language of nearly all numerics.

8 skills 0 questions ← whole tech tree

Content for this course is still being written. For now, explore the skill map below — every node links to its full page.

Skill map

Each node is a skill; an arrow means "learn this first." Deep-dive links go to the full pages.

Matrix Storage

Row- vs column-major: the layout under the math.

content coming soon
Gaussian Elimination

Solve Ax=b by row reduction with pivoting.

content coming soon
Power Iteration

Find the dominant eigenpair by repeated multiplication.

content coming soon
deep dive ↓Power Iteration
Condition Number

How sensitive is the solution? Stability and precision.

content coming soon
QR Factorization

Stable factorization for least-squares and eigenvalues.

content coming soon
Conjugate Gradient

Iterative solver for symmetric positive-definite systems.

content coming soon
deep dive ↓Conjugate Gradient
Krylov / Arnoldi

Orthonormal bases of Krylov subspaces for large problems.

content coming soon
deep dive ↓Arnoldi Iteration
Lanczos Iteration

Symmetric Arnoldi: tridiagonal compression of an operator.

content coming soon
deep dive ↓Lanczos Iteration