Matrices · geometric meaning · explainer

Columns tell where î and ĵ go

A is built from where î and ĵ go. Then Av is that same mix of those two image columns — drag v to see it.

col₁ = Aî col₂ = Aĵ

Stage 1 — only the image columns. Press Next when ready.

Stage

The two columns of A are the images of the basis vectors î and ĵ.

Matrix A

1
0.5
0.25
1.5

Working