Prof. Denis Auroux
Cross Product
Part 1

Part 2
“…Can you sort of think about
9 vectors in 9 dimensional space
and take their combinations?
That's really the central thought that
you get kind of used to in linear algebra.
Even though you can't really visualize it,
you sort of think you can after a while.
Those 9 columns and all their combinations
may very well fill out the whole 9 dimensional
space.
But if the 9th column happened to be the same
as the 8th column and gave nothing new,
then probably what it would fill out would be
… I hesitate even to say this … it would be
a sort of plane, an 8 dimensional plane inside
9 dimensional space.
And it's those 8 dimensional planes
inside 9 dimensional space that we have
to work with eventually…”
Icosahedral Sphere
Equalarea pixelization of the sphere
(with constant Jacobian)
TNT/JAMA
QR factorization using Householder matrices