Re: SQL Trees

Mikito Harakiri wrote:
> Speaking of transpose, here is a cute property:
>
> Let mirror path be the path in the reverse order. For example, the reverse
> of
>
> 1.1.2
>
> is
>
> 2.1.1
>
> They have reverse matrix representations! In the above case transposed
> matrix
>
> [[5,2],[3,1]]
>
> is
>
> [[5,3],[2,1]].
>
> Naturally, palindrome paths correspond to symmetric matrices.

Easy to prove by [strong] induction. Let

X=[[a,b],[c,d]]

Y=[[e,f],[g,h]]

Then

X*Y=[[ae+bg,af+bh],[ce+dg,cf+dh]]

and

Y^T*X^T=[[e,g],[f,h]]*[[a,c],[b,d]]=[[ae+bg,ce+dg],[af+bh,cf+dh]] Received on Mon Jun 07 2004 - 13:57:55 CDT