determin.ant
Free · No sign-up · Open source

Linear algebra,
finally explained with pictures.

Most courses throw you into equations. We start with arrows. Every concept is interactive — drag things around and build the intuition before you touch any formula.

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Complete beginners
Never studied linear algebra. That's fine — we start from zero.
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CS undergrads
You know arrays. A vector is an array. Let's go from there.
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ML practitioners
Finally understand why matrices multiply the way they do.

Course modules

8 modules · 38 lessons · All free

01

Vectors

available

What is a vector? Learn to think geometrically before algebraically.

What is a vector?Vector additionScalar multiplicationLinear combinationsSpanLinear independenceCross product
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02

Transformations

available

Matrices aren't grids of numbers — they're instructions for moving space.

What is a transformation?Matrices as transformationsCompositionThe transformation zooBuild your own
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03

Systems of Equations

available

Finding where lines (and planes) intersect — geometrically and algebraically.

Geometric interpretationGaussian eliminationLU decompositionTypes of solutions
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04

Determinants

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What does a matrix do to area? The determinant tells you.

Area scalingThe zero determinantInvertibility
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05

Vector Spaces

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The bigger picture: bases, dimensions, and the spaces matrices create.

Basis and dimensionColumn, null, and row spaceRankRank-Nullity theoremChange of basis
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06

Eigenvalues

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Some vectors don't change direction under a transformation. Those are special.

Eigenvectors — the intuitionThe characteristic polynomialComplex eigenvaluesDiagonalizationPositive definite matricesMarkov chains
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07

Orthogonality

available

Perpendicularity, projections, and how to find the closest point to a line.

Dot productProjectionGram-SchmidtLeast squares
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08

SVD

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Every matrix is a rotation, a stretch, and another rotation. This is SVD.

Rotate, stretch, rotateSVD explorerMatrix normsImage compression
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