Eigenvectors
A·v = λ·v — the unit circle becomes an ellipse, eigenvectors are its principal axes. Interactive vector, exact eigenvalue computation, every special case: real, complex, defective, singular.
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Linear algebra Learn interactively.
Grasp matrices, vectors and linear maps interactively
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Gaussian elimination step by step
Perform row operations with exact fractions, reach echelon form and back-substitute. Explore unique, absent or infinitely many solutions, matrix inverses and intersecting planes.
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Matrix × vector
How a 2×2 or 3×3 matrix deforms space — point clouds, grid distortion and basis vectors in split-screen (2D + 3D).
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Matrix multiplication
A·B as composition: three columns Original | B·v | A·B·v show how two linear maps are chained — with a swap button for A·B ≠ B·A.
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Tesseract — the cube of the fourth dimension (3D)
A 4D cube turns in a chosen plane and is projected into space: in an xw, yw or zw rotation the inner cube seems to turn inside out, although all 32 edges stay equally long in 4D. A true slice with the hyperplane w = c shows what a 3D being would see. Exhibit-ready: also stands on a plinth in "Knowledge as space".
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