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Interactive 3D/Matrix Transformations in 3D
Loading 3D scene…
● Original·● Transformed
XYZbasis vectors (solid = original, dashed = transformed)
3×3 Matrix
det = 1.0000
Presets
No transformation - every vector maps to itself.
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Each column of the matrix tells you where a basis vector lands. The determinant tells you how volume scales - negative means orientation flips.
Try: Apply "Reflect Y" then "Rotate 45°" - matrices compose by multiplication (order matters!).

Matrix Transformations in 3D - Interactive Visualization

Every neural network layer applies a matrix transformation to its input vectors. This visualizer makes the abstract concrete: enter a 3×3 matrix and watch it reshape a unit cube in 3D space. Presets show the five most important transformation types used in machine learning and computer graphics.

  • Rotation matrices: see how orthogonal matrices preserve distances and angles
  • Scale matrices: understand how diagonal matrices stretch or compress space
  • Shear transformations: key to understanding affine transformations in CNNs
  • Singular matrices: watch space collapse when the determinant is zero
  • Basis vectors X, Y, Z and their transformed equivalents shown as colored arrows
  • Foundation for PCA, SVD, attention mechanisms, and all of deep learning

Part of the EngineersOfAI Interactive 3D - free interactive visualizations covering every major concept in machine learning and AI engineering. Hover any element for a plain-English explanation. No code required.