← Math simulations  ·  EE263, Stanford

Two views of y = Ax: rows and columns

The same equation has two readings. By rows (input space, left): each yi = ãi⊤x is a line, and x is where they meet (the rows are “sensors”). By columns (output space, right): y = x1a1 + x2a2, the output is a mixture of the columns of A (the “actuators”). Drag x on the left or y on the right; watch both pictures move.

Matrix A

A =

Type entries, or pick a preset.

x (drag left)(1.00, 2.00)
y = Ax (drag right)(4.00, 1.00)
det A+3.00

Presets

column a1   column a2
row line 1   row line 2
the points x and y

Input space  rows as lines; x is the intersection

Output space  y = x1a1 + x2a2