How to compute k'th tensor power of matrix

Question

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 $M$.

Answer 1

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.