# Are matrices in $\rm SU(2) \times \rm SU(4)$ unitary?

I want to ask about unitary group $\rm SU(2)$ and $\rm SU(4).$

From my reading, the matrix of $\rm SU(2)$ and $\rm SU(4)$ is unitary matrix.

I make the product of $\rm SU(4)\times SU(2)$

It is possible when I make an evolution, the matrix of $\rm SU(4)\times SU(2)$ is not unitary?

• That's not the tensor product. It's just the Cartesian product. – user1504 Oct 13 '16 at 18:20
• For an explanation of user1504's comment, see e.g. this Phys.SE post. – Qmechanic Oct 13 '16 at 18:55
• @user1504, how to make the cartesian product between SU(4)×SU(2) since it cannot be multiply because not same order. please help me – munirah Oct 15 '16 at 0:40
• The cartesian product is the set of pairs $(g,h)$, with $g\in SU(4)$ and $h \in SU(2)$. Multiplication on the Cartesian product is element-wise; $(g,h) (g',h') = (gg', hh')$. – user1504 Oct 15 '16 at 9:32
• it will have a 8x8 matrix? but how?. can u give me example for SU(2)xSU(2). and what it mean by g' and h' – munirah Oct 15 '16 at 9:35

It is possible [..] the matrix of $\rm SU(4)\times SU(2)$ is not unitary?