prove the identity of the kronecker product of four matrix

Asked Oct 29 '14 at 06:35

Active Oct 29 '14 at 07:21

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Suppose that $H_i$($i=1,2,3,4$) are four arbitrary matrices, the Kronecker product relation below $$ (H_1\otimes H_2)\otimes(H_3\otimes H_4)=H_1\otimes (H_2\otimes H_3)\otimes H_4 $$ holds due to the fact that $(H_1\otimes H_2)\otimes H_3=H_1\otimes (H_2\otimes H_3)$. But how can we prove it directly?

edited Oct 29 '14 at 07:21

asked Oct 29 '14 at 06:35

Roger209

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Just FYI: the plural of matrix is "matrices" – terrace Oct 29 '14 at 06:53
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@TerrenceTown: Tks a lot. – Roger209 Oct 29 '14 at 07:22
To prove associativity, simply verify the equality entrywise. – user1551 Oct 29 '14 at 08:42

prove the identity of the kronecker product of four matrix

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