2.5 Eigenvalues and Diagonalisation

Question 1

Suppose A is a square matrix, if there is a non-zero vector v and a value lamda for which Av = lamda(v)

What are v and lamda

Answer 1

v is an eigenvector of A
lamda is an eigenvalue

Question 2

EIGENVECTOR STUFF

Question 3

What does it mean for two matrices A and B to be similar?

Answer 3

B = (P^-1)AP for some invertible matrix

Question 4

What is a diagonal matrix

Answer 4

A matrix A is said to be diagonalisable if it is similar to a diagonal matrix.

D = (P^-1)AP for some diagonal matrix D and some invertible matrix P

If we can do this, the eigenvalues of A will be the diagonal elements of D