Algebra·Course

Linear Algebra

Linear algebra: vector spaces, matrices, determinants, eigenvalues, linear transformations, and ML applications

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8

Modules

24

Articles

~2 h

Reading

IV

CLOs

§ 01 — Curriculum

8 modules.

Each module is a small unit. Most read in sequence — but a determined reader can begin anywhere.

M I
Complex Numbers, Matrices, and Determinants
Complex numbers, matrix operations, determinants and their properties
3 articles
18 min
Begin →
M II
Groups, Rings, and Fields
Basic algebraic structures and their properties
3 articles
18 min
Begin →
M III
Vector Spaces
Basis, dimension, linear maps, matrix of a linear map
3 articles
18 min
Begin →
M IV
Linear Operators and the Jordan Form
Invariants of operators, Jordan normal form
3 articles
18 min
Begin →
M V
Euclidean and Unitary Spaces
Inner product, orthogonalization, self-adjoint operators
3 articles
18 min
Begin →
M VI
Tensor Algebra
Multilinear forms, tensor product, tensors in physics
3 articles
18 min
Begin →
M VII
Group Theory: Sylow Theorems
Normal subgroups, Sylow theorems, solvable groups
3 articles
18 min
Begin →
M VIII
Tensor Algebra and Sylow Theorems (Advanced)
Modules, categories, homological algebra
3 articles
18 min
Begin →

§ 02 — Learning outcomes

4 outcomes.

CLO I

Matrices and Systems

Solve systems of linear equations using Gaussian elimination and compute determinants.

CLO II

Vector Spaces

Work with bases, dimension, and linear mappings.

CLO III

Eigenvalues

Find eigenvalues and eigenvectors and diagonalize matrices.

CLO IV

Applications

Apply linear algebra to problems in data analysis, optimization, and physics.

§ 03 — Practices

Begin the course

First article of the first module.

All key concepts, one page.

An AI tutor that knows the syllabus.

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