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## Complex matrix computation

New Contributor III
Hi qbies,

May I know if there is any existing libraries to perform computation with complex matrices (matrices whose elements are complex numbers)?

q can perform real number matrix arithmetic natively. Libraries like qml can help with performing more complex calculations with real matrices.

While it's trivial to implement simple complex number arithmetic in q, doing so for complex number matrices is tedious. So I wonder if there is any prior work in this area.

Best regards,
Freddie
5 REPLIES 5
New Contributor
Hi Freddie,

Unfortunately I do not believe there is currently anything available that will do what you want.

Kind Regards,
Andrew
New Contributor
what arithmetic/calculations do you need?

New Contributor III
Operands: complex numbers, complex vectors, complex matrices (vectors/matrices whose elements are complex numbers)
Operations: plus/minus, multiplication, matrix inversion
New Contributor
there's a trick to code complex numbers as real matrices   http://www.sosmath.com/matrix/complex/complex.html
using a+bi is like (a;b;-b;a) we can do addition and multiplication as
q)x:(0 1.;-1 0.)  /0+i
q)y:(1 2.;-2 1.)  /1+2i
1  3
-3 1
q)x mmu y  /complex multiplication
-2 1
-1 -2

x div y is x mmu inv y
complex matrix multiplication: i shouldn't really publish this as i haven't checked it

q)cmmu:{x{sum(mmu).'flip(x;y)}/:\:flip y}
q)0N!cmmu[((p;y);(x;y));((x;y);(p:(4 4.;-4 4.);y))];
(((-8 16f;-16 -8f);(-7 16f;-16 -7f));((-5 12f;-12 -5f);(-5 5f;-5 -5f)))

New Contributor III
Thanks for the pointer, effbiae!

I'll give it a try and see how far I can get the problem solved without a messy introduction of binary libs.