eig
Eigenvalues and eigen vectors of matrices.
`e=eig(x)`
`(c,em)=eig(x)`
`e=eig(x,y)`
`(c,em)=eig(x,y)`
 Inputs `x` A square matrix. `y` A square matrix of the same size as `x` . Outputs `e` The vector of eigenvalues of `x` or the pair `(x,y)` . `c` The matrix of eigenvectors of `x` or the pair `(x,y)` . `em` The diagonal matrix of the eigenvalues of `x` or the pair `(x,y)` .

Description
The outputs `c` and `em` are the same size as the input. For a single input, the outputs satisfy
`    x*c=c*em.`
For two inputs (the generalized eigenvalue problem), the outputs satisfy
`    x*c=y*c*em.`

Example
```>>a=complexRandn(4,4)*20;
>>a
Columns 1 through 3
1.3626 -  1.8973i     -29.0985 - 15.5639i      -9.8520 - 29.8157i
5.2219 -  4.5395i       0.2512 + 31.0335i       1.4211 + 23.2440i
8.7877 + 32.4650i      -4.9224 +  4.0209i      -9.1028 +  6.2764i
-12.9227 + 12.1951i     -18.6741 +  8.0302i       4.9407 +  4.6863i
Column 4
-4.9716 +  1.2286i
4.1932 - 17.4782i
-0.2930 -  1.7962i
1.1016 -  9.7947i

>>[c,d]=eig(a)
>>c
Columns 1 through 3
-0.6817 +  0.0856i      -0.0065 -  0.3599i       0.1534 -  0.3038i
0.1128 +  0.0040i       0.4263 -  0.2789i      -0.5195 +  0.3526i
-0.0482 -  0.5456i      -0.2392 +  0.3718i      -0.1486 -  0.5850i
0.2496 -  0.3912i       0.1430 -  0.6285i      -0.3061 -  0.1786i
Column 4
0.0698 +  0.2114i
0.1790 -  0.5785i
0.3084 +  0.4977i
0.4902 +  0.0226i

>>d
Columns 1 through 3
31.2217 -  8.7005i            0 +       0i            0 +       0i
0 +       0i     -21.3899 - 11.3147i            0 +       0i
0 +       0i            0 +       0i     -12.5804 + 26.1101i
0 +       0i            0 +       0i            0 +       0i
Column 4
0 +       0i
0 +       0i
0 +       0i
-3.6388 + 19.5231i

>>norm(a*c-c*d)
1.1802e-013
>>a=rand(4,4)
>>b=rand(4,4)
>>[c,d]=eig(a,b)
>>norm(a*c-b*c*d)
2.6940e-015
```