Linear Transformations Flashcards
Week 1.10 (8 cards)
1
Q
formula for the projection of x on to a non zero vector u
A
(v.x)/(u.u) u
4
Q
what is an orthogonal projection to the x-axis
A
a function that maps a vector U = [u1 u2] to [u1 0]
5
Q
projection matrix formula
A
Pu = 1/(|u|^2) (uuT)
6
Q
square of Pu
A
Pu
7
Q
what is the function that rotates vectors x radian the the anticlockwise direction
A
[cosx - sinx]
[sinx cosx]
8
Q
how to prove a function is linear
A
apply the function to:
- f(x + y) and prove it = f(x) = f(y)
- f(cx) and prove it = cf(x)
