#flo #inclass
1 Dimension
notes, inclass, on KBxChapter2CReading.
1.0.1 number of basis
{0} is just a point! so you have zero places to move. thus, it has dimension 0, and its basis is len 0. else, you can get infinite number of basis in a vector space.
1.0.2 number of dimensions dependent on scalar field
assume a vec space is over f!
vector space \(C^1\) -> 2D if over R, and 1D if over C because you need the field of scalars!
uncountable infinity! might check it out, later.
trivial extension just means doing nothing trivial reduction just means doing nothing.
1.0.3 dimension of a sum proof! oh jeez
KBxChapter2CReading#formula for dimension of sum of two subspaces ok, reviewing it!
union of subspaces doesn't normally work well, because the result is generally not a subspace.
but it works for sets!
when two planes intersect at a line, and you sum them, then you can get anywhere in \(R^3\)?
don't want to overcount the intersecting line?
this still makes no sense.