Absolute value of a matrix...

[Rob Beezer]

... is the determinant? Does this make sense to anyone? Am I missing
something? I can't think of a reason why, and the documentation
(sage.matrix.matrix2.Matrix._abs_) does not shed any extra light on
the reason.

This came up on sage-support

http://groups.google.com/group/sage-support/browse_thread/thread/9134e0891270cb83

where Justin Walker's surmisition is that the vertical bars used as
notation for the determinant is the reason.

Shooting from the hip, I'd be inclined to remove (deprecate) this, but
would happily be corrected/illuminated.

Rob

[koffie]

On Apr 7, 5:04 am, Rob Beezer <goo...@beezer.cotse.net> wrote:
> ... is the determinant?  Does this make sense to anyone?  Am I missing
> something?  I can't think of a reason why, and the documentation
> (sage.matrix.matrix2.Matrix._abs_) does not shed any extra light on
> the reason.
>
> This came up on sage-support
>

> http://groups.google.com/group/sage-support/browse_thread/thread/9134...

>
> where Justin Walker's surmisition is that the vertical bars used as
> notation for the determinant is the reason.
>
> Shooting from the hip, I'd be inclined to remove (deprecate) this, but
> would happily be corrected/illuminated.

+1 it doesnt even satisfy the triangle inequality
>
> Rob

[javier]

If one thinks of "absolute value" as in the metric sense of "norm"
then indeed the determinant makes no sense. Some valid norms for a
matrix would be:
* The maximum of the absolute values of its entries (supremum norm)
* The root of the sum of the squares of all entries (2-norm)
* The maximum of the absolute values of the eigenvalues (spectral
radius)
and many others (including mixed by-row and by-column norms)
My personal favorite is the spectral radius, but there is no reason to
favor one in place of the others as "absolute value". And in any case
the use of the determinant is completely out of context.

Cheers
J

[Simon King]

On 7 Apr., 10:43, javier <vengor...@gmail.com> wrote:
> ... And in any case

> the use of the determinant is completely out of context.

+1.

There is one reason why one could think that the determinant should be
related with the absolute value: Both are often (at least in my
experience) denoted by vertical lines: |-5| for the absolute value of
-5, |M| for the determinant of M, in contrast to its norm, which would
be ||M||.

But |-5| is not supported in Sage. So, using "abs" to denote the
determinant makes no sense whatsoever, IMO.

By the way, *should* |-5| be supported in Sage? Via preparsing?

Cheers,
Simon

[Jeroen Demeyer]

On 2011-04-07 10:54, Simon King wrote:
> By the way, *should* |-5| be supported in Sage? Via preparsing?

Looks hard to do in a good way, because a parser cannot see the
difference between a left and right |.