MONAD GRAPhi-X

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Matice

Science lab page · one study surface at a time.

A·B · living transform

Matrix A

Orthogonal rotation around Z built from cos/sin. det = 1, so it preserves volume and length.

Matrix B

Anisotropic scaling by golden ratio powers. det = φ·1·(1/φ) = 1 — a shape stretched yet volume-preserving.

Angle θ (rotation / shear parameter)45°

0.71-0.710.000.710.710.000.000.001.00

1.620.000.000.001.000.000.000.000.62

A · B

1.14-0.710.001.140.710.000.000.000.62

B · A

1.14-1.140.000.710.710.000.000.000.62

(A·B)ᵀ transpose

1.141.140.00-0.710.710.000.000.000.62

(A·B)⁻¹ inverse

0.440.440.00-0.710.710.000.000.001.62

det(A·B)

1.000

0 ⇒ singular, negative ⇒ mirrored

trace(A·B)

2.469

sum of eigenvalues

commutativity

A·B ≠ B·A

order of transformations matters

Vector transform (A·B)·v

vx1.00

vy1.00

vz1.00

[1.00, 1.00, 1.00] → [0.44, 1.85, 0.62]