3D Vector Space & Linear Transformation Explorer

Determinant (Vol Scale): 1.000

Trace (Sum Diag): 3.000

Kernel Dimension (Nullspace): 0 (Full Rank)

Transformation Presets

Matrix Tensor (M) Real-time

m11

m12

m13

m21

m22

m23

m31

m32

m33

Spectral Decomposition

Display Options

Show Unit Cube Volume Show Transformed Grid Mesh Show Eigenvector Trajectories

Math as Spatial Transformation: Matrices are not static lookup tables. A 3D matrix acts as a continuous warp field. The Determinant measures how much a volume scales (det = 0 collapses 3D space into a flat plane or line). Eigenvectors are special invariant directions that maintain their line of direction during the warp.