MIT Cross Product

Prof. Denis Auroux
Cross Product Part 1 | Part 2

MIT Linear Algebra

“…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…”

Prof. Gilbert Strang
MIT Linear Algebra
18.06 Spring 2005
Math Articles and Software

Icosahedral Sphere
Equal-area pixelization of the sphere
(with constant Jacobian)

QR factorization using Householder matrices

“the Jacobian plays the role of a local magnification factor for areas… Determinants of this form were first discussed by the German mathematician C. G. J. Jacobi (1804–1851).”
George F. Simmons, Calculus with Analytic Geometry 2nd ed.
“The QR algorithm, dating back to the early 1960s, is one of the jewels of numerical analysis.”
Trefethen & Bau, Numerical Linear Algebra
Copyright © 2017 by 3D Software
All rights reserved