# Thread: Properties of a Basis: Eigenvectors

1. ## Properties of a Basis: Eigenvectors

b1= [1; 1; 1; 1], b2 = [1; 1; -1; -1], b3 = [1; -1; 0; 0], b4 = [0; 0; 1; -1]

Let Beta = {b1, b2, b3, b4). Beta is basis for R^4.

What n x n matrix F has the property that x = F[x]_Beta?
What n x n matrix E has the property that [x]_Beta = Ex?

I don't need any direct calculations. I only need an explanation on how to approach this question. They don't give you the x vector, so how am I supposed to figure out the matrix? Could somebody please outline the steps or procedure needed to solve this question. I've been wrapping my head around how to figure this out. It looks pretty obvious too.

2. Hint:Change of Base!

3. Originally Posted by bambamm
b1= [1; 1; 1; 1], b2 = [1; 1; -1; -1], b3 = [1; -1; 0; 0], b4 = [0; 0; 1; -1]

Let Beta = {b1, b2, b3, b4). Beta is basis for R^4.

What n x n matrix F has the property that x = F[x]_Beta?
What n x n matrix E has the property that [x]_Beta = Ex?
What does "x" mean here?

I don't need any direct calculations. I only need an explanation on how to approach this question. They don't give you the x vector, so how am I supposed to figure out the matrix? Could somebody please outline the steps or procedure needed to solve this question. I've been wrapping my head around how to figure this out. It looks pretty obvious too.

4. ## Re: Hint

are you saying I should find the inverse of [x]_beta and then multiply it by x? But what is x?