# 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_at_news.oracle.com>

Date: Mon, 07 Jun 2004 11:57:55 -0700

Message-ID: <043xc.36$7o2.127_at_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 - 20:57:55 CEST