Domain R³
Codomain R³

Linear map of space

A shape and a vector under v ↦ A·v

Rank of A
Matrix A
(
)

Effect on space

Chosen vector

Toggle the rank of A. The solid in the domain is mapped to the codomain by v ↦ A·v.
Drag the tip to choose a vector v (domain); its image A·v appears in the codomain.
rank 3 fills space; rank 2 collapses the solid onto a plane (the image); rank 1 collapses it onto a line.
Drag the background to orbit · scroll to zoom · axes labelled x, y, z.