Linear transformations & matrices — 3Blue1Brown · Essence of Linear Algebra Ch.3
Matrices as transformations of space: rotate, shear, flip, scale, and squish the grid.
Matrix
î lands on [1, 0]
ĵ lands on [0, 1]
Matrix
× v [, ] = [2, 1]
Drag the grey arrowhead on the canvas to change v
Transform the grid — Pick a preset or type matrix values directly. Hit Animate to watch the grid morph. The faint ghost grid shows the original position. Columns of the matrix = where î (blue) and ĵ (green) land.
î (blue) and ĵ (green) show where the basis vectors end up after the transformation