# Matlab Eigenvectors

1. Apr 16, 2015

### jdawg

1. The problem statement, all variables and given/known data
I think this problem is supposed to be pretty simple, but I have almost no knowledge of how to use matlab. I was told to use this function: [V,D]=eig(A) to give me the eigenvectors (columns of matrix V) and the diagonal matrix with eigenvales in the diagonal ( matrix D). I also need to check the matrix with A=VDV-1.

2. Relevant equations

3. The attempt at a solution
I don't feel like this is right, but this is what I tried:
Here is what I typed in the script:

%1
A=[1 -3 3 3; -1 4 -3 -3; -2 0 1 1; 1 0 0 0]
[V,D]=eig(A)
V.*D.*inv(V)

And here is what came out:

A =

1 -3 3 3
-1 4 -3 -3
-2 0 1 1
1 0 0 0

V =

-0.0000 0.0000 0.0000 0.5607
-0.0000 -0.7071 0.7071 -0.7476
0.7071 -0.7071 0.7071 -0.3271
-0.7071 0.0000 0.0000 0.1402

D =

0.0000 0 0 0
0 1.0000 0 0
0 0 1.0000 0
0 0 0 4.0000

ans =

1.0e+07 *

-0.0000 0 0 0
0 -1.0712 0 0
0 0 -1.0712 0
0 0 0 0.0000

Last edited: Apr 16, 2015
2. Apr 16, 2015

### kreil

You're close. The key here is that .* does elementwise multiplication (corresponding elements are multiplied, the result is the same size as the inputs), whereas * does matrix multiplication (you know, where an NxM matrix multiplied by an MxP matrix results in an NxP matrix).

You want to use * instead of .*, and when you do that you'll get a much better answer for the check:

Code (Text):

V*D*inv(V)

ans =

1.0000   -3.0000    3.0000    3.0000
-1.0000    4.0000   -3.0000   -3.0000
-2.0000   -0.0000    1.0000    1.0000
1.0000    0.0000   -0.0000   -0.0000

Since the condition number of V is rather large, calculating the inverse introduces some error, so the above matrix isn't exactly equal to A, but it's close.

Code (Text):

A - V*D*inv(V)

ans =

1.0e-07 *

-0.1285   -0.1285    0.1285    0.1285
0.1286    0.1656   -0.1386   -0.1551
-0.0052    0.0250    0.0221    0.0056
-0.0072   -0.0072    0.0072    0.0072

3. Apr 17, 2015

### jdawg

Perfect! Thanks so much!!