From vectors to eigenstructure.

Unit 1 · Building blocks

Vectors & spaces

Vectors, span, linear combinations, the geometry of ℝⁿ.

1 demo lesson · 8 cards Unit 2 · Systems

Systems of equations

Row reduction, echelon form, Gaussian elimination, homogeneous vs. particular.

1 demo lesson · 8 cards Unit 3 · Structure

Matrix algebra

Multiplication, inverses, transpose, block matrices, the rules that make it work.

1 demo lesson · 8 cards Unit 4 · Geometry

Determinants

The signed volume of a parallelepiped — and what it tells you about invertibility.

1 demo lesson · 8 cards Unit 5 · Substructure

Subspaces & basis

Column space, null space, rank-nullity, change of basis.

1 demo lesson · 8 cards Unit 6 · Transformations

Linear maps

Matrix representations, kernel, image, isomorphisms, similarity.

1 demo lesson · 8 cards Unit 7 · Inner products

Inner product spaces

Dot products, norms, orthogonality, Gram-Schmidt, projections.

1 demo lesson · 8 cards Unit 8 · Eigen-theory

Eigenvalues & eigenvectors

Characteristic polynomials, diagonalization, the spectral theorem for symmetric matrices.

1 demo lesson · 8 cards Unit 9 · Applications

Matrix decompositions

LU, QR, singular value decomposition — the algorithms data science runs on.

1 demo lesson · 8 cards