12-240/Linear Algebra - Why We Care

2012-10-31T14:32:10Z

Marie: /* Linear Algebra is the Small Scale Theory of ''Everything'' */

{{12-240/Navigation}}
==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.'''
{| align=center
|- align=center
|[[Image:06-240-QuiltBeforeMap.png|200px]]
|<math>\longrightarrow</math>
|[[Image:06-240-QuiltAfterMap.png|200px]]
|
|- align=center
|<math>z</math>
|<math>\mapsto</math>
|<math>z^2</math>
|([[06-240/QuiltPlot|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 {{Pensieve Link|Classes/12-240/index.html#MathematicaNotebooks|The Mathematica notebook QuiltPlot}}.

== Lecture notes scanned by [[User:Marie|marie]] ==
<gallery>
Image:12-240_Oct30Notes.pdf
</gallery>

File:12-240 Oct30Notes.pdf

2012-10-31T14:27:59Z

Marie: Notes for Lecture 14, October 30, 2012. Topics include: nullity, rank, kernel, image, and dimension theorem.

Notes for Lecture 14, October 30, 2012. Topics include: nullity, rank, kernel, image, and dimension theorem.

Drorbn - User contributions [en]

12-240/Linear Algebra - Why We Care

File:12-240 Oct30Notes.pdf