# A Meaning of X in SU(2)XSU(2)

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1. Oct 15, 2016

### munirah

From my reading, the X between SU(4)XSU(2) mean Cartesian product.

But How the way to mutiply two matrix A in SU(4) and B in SU(2).

Example the matrix

A=\begin{pmatrix} a & b &
c & d \\ e& f &
g & h \\ i & j &
k & l \\ m & n&
o & p \end{pmatrix}

and

B=\begin{pmatrix} 1 &2 \\
3 &4 \end{pmatrix}

Please show me the way to multiply SU(4)XSU(2) to form 8X8 matrix.

Thank you

Last edited: Oct 15, 2016
2. Oct 15, 2016

### Staff: Mentor

B should be 2x2. Technically you can form such a product by components and express it as matrix but I don't think it is useful in any way in particle physics. The entries would be "a1", a2", "a3", "a4", "b1", "b2" and so on.

3. Oct 15, 2016

### munirah

Sorry for wrong matrix. It mean, I just do the tensor product?

4. Oct 15, 2016

### Staff: Mentor

Sure.

5. Oct 15, 2016

### munirah

Thank you very much for helping me to solve my problem. Thank you again.thank you

6. Oct 15, 2016

### Staff: Mentor

Sure? I would expect a block matrix $\begin{bmatrix}A & 0 \\ 0 & B\end{bmatrix}$.

7. Oct 15, 2016

### Staff: Mentor

Representations are arbitrary, but the block matrix is probably a better model.