Drorbn at 16:27, 27 October 2009

2009-10-27T16:27:08Z

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			{{09-240/Navigation}}
	==Linear Algebra is the Small Scale Theory of ''Everything''==		==Linear Algebra is the Small Scale Theory of ''Everything''==

Drorbn at 16:26, 27 October 2009

2009-10-27T16:26:47Z

New page

==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|2009-10|The Mathematica notebook 240AlgebraI-QuiltPlot}}.

09-240/Linear Algebra - Why We Care - Revision history

Drorbn at 16:27, 27 October 2009

Drorbn at 16:26, 27 October 2009