Why do logical operators do not work with the eigenvalues of this matrix?

I am trying to find index of eigenvalues of a matrix which are equal to 1. But for some reason the '==' or 'ismember' don't work to recognize that. Can someone look at this code and suggest, what is wrong with this?

TM = [0.1,0.2,0.7; 0.5,0.2,0.3;0.1,0.1,0.8];

[V,D] = eig(TM');
V
D
vec = sum(D);

    for n1 = 1:length(vec)
        if (vec(n1) == 1)
            index_for_pop = n1;
        end
    end
index_for_pop



===output
V =

   -0.2022   -0.8100   -0.4938
   -0.1711    0.3162   -0.3162
   -0.9643    0.4938    0.8100


D =

    1.0000         0         0
         0   -0.1562         0
         0         0    0.2562

Undefined function or variable 'index_for_pop'.

Error in trial2 (line 14)
index_for_pop

Answer 1

[Christine Tobler]

There's a small round-off error on the eigenvalue 1:

>> TM = [0.1,0.2,0.7; 0.5,0.2,0.3;0.1,0.1,0.8];
[V,D] = eig(TM', 'vector');
D(1)
ans =
    1.0000

>> D(1) - 1
ans =
   4.4409e-16

It's usually not a good idea in numerical computations to do an "==" type comparison, better to use abs(D(1) - 1) < 1e-14, for example.

[Vipul Kumar]

Thanks a lot. That solves it for me. :)

Answer 2

[Steven Lord]

The eigenvalue is not exactly equal to 1. It is close enough to 1 that it is displayed as 1 in the default display format.

You might want to call eig with the 'vector' input so it returns your eigenvalues as a vector rather than a diagonal matrix.

Use ismembertol or the technique shown in the last block of code in this Answers post.