Page 55 - PowerPoint Presentation

Linear Transformations as Change of Basis

v =(v ,v ) j =(0,1)
x
y

p uv p ij

u=(u ,u )
x
y
i =(1,0)

ij
uv
p = (4,3) p = 4u+3v

p =4u +3v x ij = u x v x    4 = u x v x  uv
x
x
p =4u +3v y p  u y v y   3   u y v y  p

 



y
y

Any linear transformation is a basis!!!