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Re: SQL Trees

From: Vadim Tropashko <vadimtro_at_yho.cm>
Date: Mon, 07 Jun 2004 11:57:55 -0700
Message-ID: <043xc.36$7o2.127@news.oracle.com>


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

Original text of this message

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