Re: SQL Trees
From: Mikito Harakiri <mikharakiri_at_iahu.com>
Date: Mon, 7 Jun 2004 11:27:59 -0700
Message-ID: <YD2xc.34$7o2.220_at_news.oracle.com>
> "Vadim Tropashko" <vadimtro_at_yho.cm> wrote in message
> news:ppnwc.4$_a1.87_at_news.oracle.com...
> > ... Materialized path encoding and Farey/Continued Fractions/Moebius
> > transformations/Orthogonal 2x2 matrices. ...
> -----------------^^^^^^^^^^^
>
> They are not orthogonal. The inverse of Matrix(2,2,[[5,1],[1,0]]), for
> example, is Matrix(2,2,[[0,1],[1,-5]]) which is not transpose.
Date: Mon, 7 Jun 2004 11:27:59 -0700
Message-ID: <YD2xc.34$7o2.220_at_news.oracle.com>
"Mikito Harakiri" <mikharakiri_at_iahu.com> wrote in message
news:z51xc.25$7o2.178_at_news.oracle.com...
> "Vadim Tropashko" <vadimtro_at_yho.cm> wrote in message
> news:ppnwc.4$_a1.87_at_news.oracle.com...
> > ... Materialized path encoding and Farey/Continued Fractions/Moebius
> > transformations/Orthogonal 2x2 matrices. ...
> -----------------^^^^^^^^^^^
>
> They are not orthogonal. The inverse of Matrix(2,2,[[5,1],[1,0]]), for
> example, is Matrix(2,2,[[0,1],[1,-5]]) which is not transpose.
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.