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LAFF. week 2. Linear Transformations and Matrices (Linear transformations…
LAFF. week 2.
Linear Transformations and Matrices
Linear transformations
2D rotations
rotation and scaling
rotation and addition
Function is LT if
you can
scale/sum and rotate
or
rotate and scale/sum
Matrices
L(x) = Ax
LT(LC) = LC(LT)
problem
f: Rn --> Rm
direct
f(x) = y
y = ?
inverse
y = f(x)
x =?
eigenvalue
f(x) = lambda*x
lambda, x = ?
proof
2 vectors
L(ax + by) = aL(x) +bL(y)
since L is LT
L(ax + by) = L(ax) + L(by)
L(ax) = aL(x)
several vectors
math induction
f(k)
f(k+1)
example for
same in two directions
insight
