12-240/Linear Algebra - Why We Care
Revision as of 10:32, 31 October 2012 by Marie
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.
- 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.