THE DOT PRODUCT↗
0.71
How much do we agree?
For unit vectors, u · v = cos θ. Turn the angle to see their alignment change.
+ THE LINEAR ALGEBRA PLAYGROUND
A little math.
A lot of possibility.
Give a vector a nudge. Bend a coordinate system.
See what happens when the numbers move.
R. Feynman
A. EinsteinA FEW FAMILIAR FACES. A CLOSER LOOK ↗ Original v Transformed Av
↖ Drag the purple pointTHE DETERMINANT↖ CONNECTED TO CANVAS
det(At) = 1.00
Space has a multiplier.
The unit square now covers 1.00 square units. Its orientation is preserved.
Updates as you transform
A HAPPY LITTLE EQUATION
AᵀA = I
Orthogonal matrices
Lengths stay the same. So do angles.
The minds in the margins.
Five minds. Five worlds. Step inside a sketch and scroll through its ideas.
PhysicistFIG. 01
Albert Einstein
Space, time & relativity
PhysicistFIG. 02
Richard Feynman
Particles, paths & possibility
Chinese philosopherFIG. 03
Confucius
Ethics, learning & reflection
Chinese aerospace engineerFIG. 04
Qian Xuesen
Flight, flow & motion
Theoretical physicistFIG. 05
J. Robert Oppenheimer
A study of the atomic age
Scroll-driven worlds, drawn from remarkable ideas.AI-generated illustrations