How to identify repeated eigenvalues of a matrix?

Take the matrix A as an example:

    A = [1 1 0 0;0 1 1 0;0 0 1 0;0 0 0 3]

The eigenvalues of A are: 1,1,1,3. How can I identify that there are 2 repeated eigenvalues? (the value 1 repeated two times)

Thank you in advance.

Answer 1

[Aditya Deshpande]

You can find the number of times an eigen value is repeated as follows.

A = [1 1 0 0;0 1 1 0;0 0 1 0;0 0 0 3];
E = eig(A);
u = unique(E);
R = histc(E,u)-1;

Output is:

E =
     1
     1
     1
     3

u =
     1
     3

R =
     2
     0

NOTE: if R(i) = 0, eigen value is not repeated, but has occurred only once in vector E.

Answer 2

[Christine Tobler]

For general matrices, the eigenvalues will typically have a bit of round-off error, so repeated eigenvalues will not be exactly identical. In those cases, you should use uniquetol instead of just unique in the algorithm proposed by Aditya.

[Mohammad Ayoub]

Thank you very much for pointing that out.