You're running under warnings, you should have seen the warnings
Prototype mismatch: sub main::append: none vs (;@) at (eval 6) line 8
Prototype mismatch: sub main::i: none vs () at ./ttt line 10
The second of these indicates a conflict between CGI and (presumably) PDL::Complex. Both are apparently importing a function i() in your name space. When you put CGI and HTML generation on the side for the moment (not loading CGI and CGI::Carp, and modifying the code accordingly), you avoid the conflict. The complex matrix $matrixM is printed out fine
for me after that change. Expect the number you specify as " 2+1*i" to be printed as " [2, 1]". The output format isn't quite as intuitive as the input format.
I haven't followed your code further, except noting that it announces the inverse of $MatrixM, but prints its determinant.
Anno
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