Gilbert Strang MIT 18.06 Matrix Lab & Spatial Transformation Visualizer

Basis Vector i (1,0) → Ax_1

Basis Vector j (0,1) → Ax_2

Eigenvectors (Ax || x)

Interactive Vector x → Ax

Singular Value Decomposition (SVD: A = U Σ V^T) Full Matrix Action A

A = [[2.00, 1.00], [1.00, 2.00]]

As Gilbert Strang highlights: "SVD chooses orthogonal bases for the domain and codomain so that any linear map becomes a pure diagonal stretch."

Transformation Matrix A Direct Edit

[

a₁₁

a₁₂

a₂₁

a₂₂

]

Linear Algebra Telemetry

Determinant (det A) 3.00

Trace (tr A) 4.00

Eigenvalues (λ₁, λ₂) 3.00, 1.00

Singular Values (σ₁, σ₂) 3.00, 1.00

The Big Picture of Linear Algebra:
Matrix A multiplies vector x to give Ax. Grid lines bend, unit circles stretch into ellipses of area |det A| × π, and special lines where Ax = λx reveal the invariant eigenvectors.

Validated State Output

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