Invariant and eigen

Question 1

How do you find an equation for invariant points?

Answer 1

M[x,y] = [x,y]

Question 2

What does the line of invariant points give you if the transformation is a reflection?

Answer 2

The equation of the mirror line

Question 3

Is a line of invariant points an invariant line?

Answer 3

Yes

Question 4

Is an invariant line a line of invariant points?

Answer 4

Not necessarily

Question 5

How to find an invariant line?

Answer 5

Substitution such as y = mx,

will usually be given

Question 6

What is the relationship between eigenvectors and invariant lines through the origin? What about when lambda = 1?

Answer 6

If V is an eigenvector, the line r = tV is an invariant line through the origin, if lambda =1, it is also a line of invariant points

Question 7

What is the characteristic equation?

Answer 7

determinant M-lambdaxI = 0

Question 8

Repeated eigenvalues?

Answer 8

Two eigenvectors added together which represents an invariant plane

Question 9

When diagonalizing, what are D and U?

Answer 9

D is the two eigen values

U is the two eigenvectors put side by side