Calculating the Kronecker product

Leopold Kronecker
Image via Wikipedia

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)

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