# Making a eigenvector a linear combination of other eigenvectors

JordanGo

## 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)?

## Answers and Replies

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.

JordanGo
Ok, that makes sense, thanks a lot!

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)?