non-square matrix determinants

Thanks to Gary Morrison for the info on
how to calculate matrix determinants.

I have another question regarding them:
Suppose the matrix is not square (is there
a name for that?) - how do you calculate
that determinant? I'm thinking of a
5-limit system where more than 2 commas
vanish. For example:

| a b |
| c d |
| e f |

or

| a b |
| c d |
| e f |
| g h |

or even

| a b |
| c d |
| e f |
| g h |
| i j |

Yes, I would like explicit instructions
on how to calculate all three (like your
last ones, by example). Toss in a couple
of non-square 7-limit ones too, such as:

| a b c |
| d e f |

and

| a b c |
| d e f |
| g h i |
| j k l |

It's quite easy to use a spreadsheet
to do this stuff, once you know how.

This would have an application linked
to the info I gave in my post on
5-limit xenharmonic bridges - just so
you non-theory guys can stay interested :)

- Monzo
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On Mon, 8 Mar 1999, Joseph L Monzo wrote:
> Suppose the matrix is not square (is there
> a name for that?) - how do you calculate
> that determinant?

Mathematically, the determinant operation is only defined on square
matrices.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Well, so far, every time I break he runs out.
-\-\-- o But he's gotta slip up sometime . . . "

NOTE: dehyphenate node to remove spamblock. <*>

> I have another question regarding them:
> Suppose the matrix is not square

Best I can recall, determinants only apply to square matrices. (I
probably ought to dust off my ol' Linear Algebra book and make sure I'm
remembering this all right!)

> From: Gary Morrison <mr88cet@texas.net>
>
> > I have another question regarding them:
> > Suppose the matrix is not square
>
> Best I can recall, determinants only apply to square matrices. (I
> probably ought to dust off my ol' Linear Algebra book and make sure I'm
> remembering this all right!)

That's right, the notion of determinant only applies to square matrices. It
would be possible to extend the notion to non-squares, but the applications
are much more limited.

Vania.

Vania Mascioni ph : (1)-512-471.3149
Department of Mathematics fax : (1)-512-471.9038
The University of Texas at Austin e-mail : mascioni@math.utexas.edu
Austin, TX 78712, U.S.A. http://www.ma.utexas.edu/users/mascioni/