14-240/Linear Algebra - Why We Care

From Drorbn
Revision as of 20:38, 28 October 2014 by Drorbn (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigationJump to search

Linear Algebra is the Small Scale Theory of Everything

  • To study the large, start with the small.
  • In small scales, every space is a vector space.
    • Indeed if you walk a mile east, a mile north, a mile west and a mile south, you're back were you started, but if you fly a 1,000 miles east, a 1,000 miles north, a 1,000 miles west and a 1,000 miles south, you're not back were you started (where will you be?).
  • In small scales, every function is a linear function.
06-240-QuiltBeforeMap.png 06-240-QuiltAfterMap.png
(code)
  • The world doesn't come with coordinates.
    • Hence whenever we can we work without a basis, and when we do study bases, we study all of them.

See also The Mathematica notebook QuiltPlot.