# Making a eigenvector a linear combination of other eigenvectors

1. Sep 27, 2012

### JordanGo

1. The problem statement, all variables and given/known data
Write the eigenvector of $\sigma$x with +1 eigenvalue as a linear combination of the eigenvectors of M.

2. Relevant equations

$\sigma$x = (0,1),(1,0) (these are the columns)

3. The attempt at a solution

.... Don't know what to do. Can someone show me how to do this using arbitrary eigenvectors, say (a,b) and (c,d)?

2. Sep 28, 2012

### clamtrox

Can you find the eigenvector in question? Let's denote it by (v,w). Then you can write
(v,w) = C1(a,b) + C2(c,d) and solve the constant C's.

3. Sep 28, 2012

### JordanGo

Ok, that makes sense, thanks a lot!

4. Sep 28, 2012

### HallsofIvy

Okay, that's $\sigma$. What is M??? we can't write something "as a linear combination of the eigenvectors of M without knowing what M is!