# Making a eigenvector a linear combination of other eigenvectors

## Homework Statement

Write the eigenvector of $\sigma$x with +1 eigenvalue as a linear combination of the eigenvectors of M.

## Homework Equations

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

## 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)?

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.

Ok, that makes sense, thanks a lot!

HallsofIvy
Homework Helper

## Homework Statement

Write the eigenvector of $\sigma$x with +1 eigenvalue as a linear combination of the eigenvectors of M.

## Homework Equations

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

## 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)?