linear algebra week2 Changing th

Changing the basis

coordinate system(7) = 7
unit length(2) = 2
basis vectors(14) = 14 (used to define vector)

new basis(7) = 7

we'll look at what we mean by coordinate systems and we'll do a few cases of changing from one coordinate system to another.

orthogonal(4) = 4
新的basis vector(如果不是相互正交的)需要使用matrice，以后会讲到该点。

Basis, vector space, linear independence

basis(16 + 1 basic vector) = 17
linear independence(3) = 3 combination(8) = 8
dimension(5) = 5

mean(6) = 6
 1.A basis is a set of n vectors that are not linear combinations of each other, which means they're linearly independent.
 2.they span the space that they describe

map(3) = 3 grid(6) = 6 spaced(3) =3

If the new basis vectors aren't orthogonal, then to do the change from one base to another, we won't just be able to use the dot product anymore,and use matrice instead.