Comment #21 on issue 2225 by pr...@goodok.ru: Enhancing Matrix Norm
http://code.google.com/p/sympy/issues/detail?id=2225
For even very simple matrices they're often hideous.
But for many collections of matrices (and for many objects), one might
could say for group of them, the norm (of appropriate kind) is very simple
and even can be equal 1. Even in the case of complicated symbolic objects.
Norm is very significant part of mathematics, not only for statistics, not
only for comparison of "length" of objects, not only if they are numeric.
For some objects p=2 important, for some objects another norm, for others
another multi-linear form as norm can be used. Norm can define space.
E.g for me, it will be useful if I can check that something has a norm ,
and after some manual transformations this norm remains saved (e.g with
multiplication it saved automatically).
I think that the following would be ideal behaviour:
Yes, indeed, "max" applied to a big number of symbols is rarely used in
symbolical algebra or not convenient.
But what behaviour will be in case of if the Frobenius norm will be as
default?
I just want to say, that I originally have just wondered that your have
chosen complicated kind of norm as default for this method.
And about what do consider as an standard. In mathematics there are no
standards, rather definitions.
I am just now checked with [1], and have determined that `norm` is defined
as something that greater than zero and have others relation properties.
And I think that, what do the concrete norm to consider as standard in
SymPy is rather a question of SymPy.
In my opinion more convenient the Frobenius norm, because of usage of `max`
is not convenient.
Or permit only explicitly specified obligatory parameter.
And what about `Norm(matrix)`, I don't understand straight away the
difference between `Matrix` and `Norm(matrix)`, and the difference between
`Matrix.norm()` and `Norm(matrix)._something_()`. Rather may be an Max
object needed which can maintenance a list in case if norm resulted max.
Finally, I don't see a big danger now, if an user will use .norm()
inappropriate.
If user do not understand or do not know what he do, when he will see a
monster formula then he will obtain the result about his knowledge anyway.
(By the way, this questions can be significant only for `live.sympy.org`,
but it can be solved with the help of another technicals)
[1] http://en.wikipedia.org/wiki/Matrix_norm
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