You can install PDL-LinearAlgebra if you want to do linear algebra over complexes. Here is an example (note that if you load PDL::LinearALgebra the x operator (matrix multiplication in PDL) is overriden by the BLAS matrix multiplication and thus is complex aware. Here is a perldl session:

perldl> use PDL::Complex
perldl> use PDL::LinearAlgebra

perldl> $matrixM = cplx pdl [ [ 1+1*i, 2+1*i], [ 1-2*i, 2-1*i] ];

perldl> p $matrixM

[
 [1 +1i  2 +1i]
 [1 -2i  2 -1i]
]


perldl> $matrixB_assigned_value = cplx pdl [ 5+8*i, 10-5*i ];

perldl> p $matrixB

[
 [ 5 +8i]
 [10 -5i]
]

perldl> msolve($matrixM,$matrixB)

[
 [3+1i]
 [2+1i]
]
 
[
 [   1   -2i     2   -1i]
 [-0.2 +0.6i   1.8 -0.4i]
]
 [2 2] 0
perldl> scalar msolve($matrixM,$matrixB)

[
 [3+1i]
 [2+1i]
]

perldl> $matrixM->minv x $matrixB

[
 [3     +1i]
 [2     +1i]
]
[download]

In the last result we see from the amount of space between the real and imaginary part that the result is less precise.

-----------------------------------------------------------
perldl> help minv
  minv
    Compute inverse of a general square matrix using LU factorization.
    Supports inplace and threading. Uses getrf and getri or cgetrf and
    cgetri from Lapack and return "inverse, info" in array context.

     PDL(inv)  = minv(PDL)

     my $a = random(10,10);
     my $inv = minv($a);

    Docs from /usr/lib/perl5/PDL/LinearAlgebra.pm

perldl> help msolve
  msolve
    Solve linear system of equations using LU decomposition.

            A * X = B

    Returns X in scalar context else X, LU, pivot vector and info. B
    is overwrited by X if its inplace flag is set. Supports threading.
    Uses gesv or cgesv from Lapack.

    (PDL(X), (PDL(LU), PDL(pivot), PDL(info))) = msolve(PDL(A), PDL(B)
+)

     my $a = random(5,5);
     my $b = random(10,5);
     my $X = msolve($a, $b);

    Docs from /usr/lib/perl5/PDL/LinearAlgebra.pm
[download]

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