eig is not giving a matrix for left eigenvectors

I am trying to find the left and right eigenvectors of a 16 by 16 matrix with [V,D,W]=eig( mat ); V, and W are supposed to be matrices where the column vectors are the right and left eigenvectors, and while V meets this, W is a 1 by 16 row vector, W =

     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16

I haven't included the matrix itself because of its size but I can. Some assistance would be much appreciated.

[John D'Errico]

Why not attach the matrix as a mat file? 16 by 16 is NOT large. In fact, it is trivially tiny.

Answer 1

[Walter Roberson]

You are using vpa() around a series of rational and floating point values. The end result of vpa() is a symbolic matrix. You are then invoking eig on a symbolic matrix, getting the symbolic eig rather than the numeric eig.

If you want the numeric eig, then skip the vpa() call.

[Samantha Zimmerman]

is there any way I could get around it with it still being symbolic? The matrix is really the result of a long series of computations involving symbolic variables; do you know of a way to make that result numerical?

[Samantha Zimmerman]

I mean i know I could make it double, but is there anything with more precision? when I try float on the double'd matrix I get

Error using float (line 46) The input argument to float was not a supported type. The only recognized strings are 'single' and 'double'. The input type was 'double'.

[Walter Roberson]

Sorry, I do not know how to calculate "right" eigenvectors symbolically.

The routine you are invoking is this one whereas you are instead reading about the numeric one over here

Your array is not going to be high precision the way you have defined it. When you use something like

vpa(A/B)

with numeric constants A and B, then A/B will be calculated in double precision and then the result will be converted to sym(), exactly as if you had done

C = A/B;
vpa(C)

In order to get high precision in a literal array, you need to use, for example,

sym(373535501472003)/sym(175921860444160000)

and even better would be

sym('373535501472003')/sym('175921860444160000')

to avoid the possibility of loss of precision with numbers larger than 2^53. For example, 37353550147200301 cannot be represented exactly in double(), with the closest number being 37353550147200304 .

If your inputs are already class sym() then you do not need to worry about this, but it applies to the sample matrix you posted, which is numeric before you vpa() it.

Answer 2

[John D'Errico]

It works well enough for me, doing exactly as I would expect on a random matrix.

clear
[V,D,W] = eig(rand(16));
whos
  Name       Size            Bytes  Class     Attributes

    D         16x16             4096  double    complex   
    V         16x16             4096  double    complex   
    W         16x16             4096  double    complex

So, if you are getting something completely different, then you need to show clearly what you did. You should attach the matrix as a .mat file to a comment.

[Samantha Zimmerman]

haha true I know its tiny its just a pain to display; i hadn't thought of attaching it in another file. Here's the code.