Calculating Eigenvalues and Eigenvectors

[niketa_gandhi]

While watching the video calculate eigenvalues and vectors and trying it for the 2 by 2 square matrix example [[9 4], [4 3]].

I got most of it except when the eigenvalue is equal to 1, the eigenvector I get is [1 -2] instead of [-1, 2].

I solved as follows

[[9 4], [4 3]] * [x , y] = 1 * [x, y]

and we get the following equations

9x + 4y = x and 4x + 3y = y

Starting with 4x + 3y = y we get y= -2x

Substituting this value

9x + 4(-2x) = x

Hence x = 1 and y = -2

[paulinpaloalto]

Well, note that if

9x + 4(-2x) = x

That reduces as follows:

x = x

right? So any value of x will satisfy that. Why choose x = 1? You could as easily choose x = -1.

The point (pun intended) is that an eigenvector is just a direction. They are not unique.