Spatial Linear Algebra — the pixels are the vectors

A 2×2 matrix is a recipe for moving space. The columns say where the basis vectors land: î → (a, c), ĵ → (b, d). The image lives on the unit square; every pixel rides the same transform. Determinant = how much area is stretched (negative = the space flips over). Edit the matrix, or solve the problems.

the matrix M

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example problems

Pixels sampled through M⁻¹ into an ImageData buffer (nearest-neighbour, pixelated upscale). Companion to the Graphical-Linear-Algebra studies — this is the matrix side of the same idea: the picture is the computation.