Solve Matlab Eigenvectors Homework

[jdawg]

Homework Statement

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.

Homework Equations

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 0V =

-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 0.1402D =

0.0000 0 0 0
0 1.0000 0 0
0 0 1.0000 0
0 0 0 4.0000ans =

1.0e+07 *

-0.0000 0 0 0
0 -1.0712 0 0
0 0 -1.0712 0
0 0 0 0.0000
[/B]

 

[kreil]

%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)

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:

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.

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

 

[jdawg]

Perfect! Thanks so much!