# Calculating the Kronecker product

I realise in my previous blog post, I showed a Kronecker product, but did not explain how it was created, so here goes.

$Let \ K_1 = \left( {\begin{array}{cc} a & b \\ c & d \\ \end{array}} \right)$

$Let \ K_2 = \left( {\begin{array}{ccc} z & y & x \\ w & v & u \\ t & s & r \\ \end{array}} \right)$

Then $K_2 \otimes K_1 = \left( {\begin{array}{cccccc} za & zb & ya & yb & xa & xb \\ zc & zd & yc & yd & xc & xd \\ wa & wb & va & vb & ua & ub \\ wc & wd & vc & vd & uc & ud \\ ta & tb & sa & sb & ra & rb \\ tc & td & sc & sd & rc & rd \\ \end{array}} \right)$