1
$\begingroup$

Is there a 1-liner to compute $M^{\otimes k}$ where $M$ is some matrix and $\otimes$ is the Kronecker product? The documentation says I can write

Z = {{1,0},{0,-1}};
KroneckerProduct[Z,Z]

What I'd like is some way (eg a function KroneckerPower[M_,k_]) that does this for $k$ copies of $M$.

$\endgroup$
3
  • $\begingroup$ KroneckerPower[m_, k_] := KroneckerProduct @@ Table[m, k] $\endgroup$
    – Natas
    Nov 12, 2020 at 17:55
  • $\begingroup$ @Natas that does what I asked for. An additional annoying feature that I hadn't anticipated when I asked is that this gives an error if you call ```KroneckerPower[M,1]''' whereas I'd like it to return M. I guess I can just explicitly define the k=1 behaviour though? $\endgroup$
    – jacob1729
    Nov 12, 2020 at 18:03
  • $\begingroup$ Sure, just define the special cases separately. The Mathematica pattern matcher will (usually) figure out which patterns are more specific. In this case defining KroneckerPower[m_, 1] := m should do what you expect. $\endgroup$
    – Natas
    Nov 12, 2020 at 21:03

1 Answer 1

2
$\begingroup$

In addition to Natas' answer, you could also try:

kp[m_, k_] := Nest[KroneckerProduct[#, m] &, m, k - 1]

or

kp[m_List, k_Integer?Positive] := Nest[KroneckerProduct[#, m] &, m, k - 1]

These should give you the exact same answer. Using Nest doesn't really save you any characters over Table, but it is a useful function so I thought I'd use it here. Nest applies the function (KroneckerProduct here) repeatedly to the previous output of Nest. I also use k - 1 so that when you enter 1 for k, you just get back m.

In the second one I'm just showing how you can add checks to the function so that it only runs if m is a List and k is an Integer greater than 0. It might not matter here, but I often end up running code where I accidentally feed a function the wrong kind of data and then Mathematica sits there printing errors until I abort.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.