Unnormalizing a matrix from eig function

How would you go about unnormalizing the v matrix in [v,e]=eig(A)?

Example:

A = [0 1 0 ;...

0 0 1 ;...

-15 -23 -9];

[v,e] = eig(A);

normalized:

v = [0.577350269189626 0.104828483672192 0.0391930900834810

-0.577350269189626 -0.314485451016576 -0.195965450417405

0.577350269189626 0.943456353049726 0.979827252087026]

wanted:

[1,1/25,1/9;

-1,-1/5,-1/3;

1,1,1]

attempted:

v/v(1) but gave

[1 0.181568259800641 0.0678844233302130

-1.00000000000000 -0.544704779401923 -0.339422116651065

1.00000000000000 1.63411433820577 1.69711058325533]

Answer 1

[Steven Lord]

Q = v./max(v, [], 1);

Display it using format rat and you'll see it matches the form you wanted (modulo the fact that you swapped the second and third eigenvectors.) This won't change how Q is stored just how it's displayed. You can also check that Q is still a matrix of eigenvectors.

r = A*Q-Q*e % All elements should be small

If you turned on format rat before displaying r, you're going to need to switch to a different display format to see that the elements of r are small.