matrix-decomposition #

Visualizes matrix factorization by fading between LU (A = L·U, with an optional P pivot hint) and QR (A = Q·R with QᵀQ = I). Animated cell sweeps suggest the stepwise construction of factors, and the bottom pipeline shows how solving A x = b reduces to simple forward/back triangular solves (LU) or projection + backsolve (QR).

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

01.Fast solving of many linear systems via triangular factors (numerical simulation, circuit solving)
02.Least-squares fitting and regression using QR (overdetermined systems)
03.Determinants/inverses and stability improvements via pivoting (P·A = L·U)

technical notes #

Pure Canvas2D, time-based 4s cycle. Matrices are 4×4 blocky grids with triangular masks; values are deterministic pseudo-random fills for texture (not computed decompositions). Uses responsive scale = min(w,h)/240 and pixel/grid snapping for a retro aesthetic; easing controls sweeps and cross-fades.

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