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Re: gruppi

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Il 18/03/2025 18:19, Stefan Ram ha scritto:
...
>    Ecco una citazione che illustra bene la visione del mondo di questi
>    fisici. ...

> |A vector comprises a set of numbers (called its components)
> |that do change under a rotation of the coordinate axes – but
> |they do so in precisely the same manner as the coordinates of
> |any point themselves change.
> "A Miscellany of Mathematical Physics" (2018) - V. Balakrishnan.

Mi sembra che si dovrebbe anche considerare lo scopo dell'autore...
Ecco una citazione più estesa:

The usual (high school!) scalars and vectors that we have considered are actually defined
with respect to the set of rotations of the coordinate axes. The value of a scalar thus defined
(e.g., the distance of a point from the origin of coordinates) does not change at all under such a
rotation. A vector comprises a set of numbers (called its components) that do change under a
rotation of the coordinate axes – but they do so in precisely the same manner as the coordinates
of any point themselves change. Indeed, this is the very definition of a vector of the usual kind.
Tensors of higher rank (2, 3, . . . ) are defined in an analogous manner; they have (slightly) more
involved transformation properties under rotations of the coordinate axes. In technical terms:
the scalars and vectors I have used so far (except for the general cases mentioned briefly on
occasion) are actually scalars and vectors under the group of proper rotations in d-dimensional
Euclidean space. Now that we have become quite familiar with scalars and vectors of this kind,
the statement just made should be much easier to digest. As my whole aim has been to provide
a simple, heuristic approach to some aspects of vector analysis, we have preferred to mention
these issues at this stage, rather than to open the discussion with them. I have also glossed
over many mathematical technicalities wherever these have not been directly relevant to the
point being made. For instance, I have not made a careful distinction between the elements of
a linear vector space and those of the dual vector space, i.e., between vectors and co-vectors,
or – in a different language – between vectors and one-forms

Cito anche dalla prefazione:

The articles themselves grew out of the notion that the mathematical
tools and techniques required by the students of physical sciences can, and should, be introduced to them in a more ‘user-friendly’ style than 
is generally the case. The initial introduction
should be heuristic, with adequate motivation. The development of the subject matter should
help the student not only to learn the techniques, but also to gain insight and the ability to
recognise interconnections. Attention should be paid to the natural unfolding of the subject
matter; one thing should lead to another. While correctness can never be sacrificed, formal
rigour and exactitude need not be at the forefront

Secondo me, quello stile poco "matematico" è voluto,
non dovuto a ignoranza dell'autore.

Ciao

-- 
Giorgio Bibbiani

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gruppi SuDo <SuDO@SuDo.net> - 2025-03-18 11:38 +0100
  Re: gruppi Giorgio Pastore <pastgio@units.it> - 2025-03-18 12:24 +0100
    Re: gruppi SuDo <SuDO@SuDo.net> - 2025-03-18 13:02 +0100
      Re: gruppi pcf ansiagorod <eelon.isthebestELIMINAMI@libero.it> - 2025-03-18 13:30 +0100
        Re: gruppi SuDo <SuDO@SuDo.net> - 2025-03-18 13:50 +0100
        Re: gruppi Marco C. <dronerosso1@gmail.com> - 2025-03-18 14:22 +0100
          Re: gruppi Marco C. <dronerosso1@gmail.com> - 2025-03-18 14:29 +0100
          Re: gruppi pcf ansiagorod <eelon.isthebestELIMINAMI@libero.it> - 2025-03-18 14:45 +0100
            Re: gruppi Marco C. <dronerosso1@gmail.com> - 2025-03-18 16:45 +0100
              Re: gruppi pcf ansiagorod <eelon.isthebestELIMINAMI@libero.it> - 2025-03-18 20:26 +0100
      Re: gruppi Giorgio Bibbiani <giorgiobibbiani@tin.it> - 2025-03-18 15:33 +0100
        Re: gruppi SuDo <SuDO@SuDo.net> - 2025-03-18 15:47 +0100
          Re: gruppi Giorgio Bibbiani <giorgiobibbiani@tin.it> - 2025-03-18 18:51 +0100
          Re: gruppi Pangloss <elioproietti42@gmail.com> - 2025-03-18 20:11 +0000
            Re: gruppi Pangloss <elioproietti42@gmail.com> - 2025-03-19 07:29 +0000
              Re: gruppi Pangloss <elioproietti42@gmail.com> - 2025-03-19 12:47 +0000
  Re: gruppi pcf ansiagorod <eelon.isthebestELIMINAMI@libero.it> - 2025-03-18 13:56 +0100
  Re: gruppi Lynkx <lynkxer@abc.it> - 2025-03-18 14:36 +0100
  Re: gruppi Marco C. <dronerosso1@gmail.com> - 2025-06-08 15:07 +0200
  Re: gruppi Giorgio Bibbiani <giorgiobibbiani@tin.it> - 2025-06-08 19:05 +0200
    Re: gruppi Giorgio Bibbiani <giorgiobibbiani@tin.it> - 2025-06-08 20:48 +0200
      Re: gruppi Giorgio Bibbiani <giorgiobibbiani@tin.it> - 2025-06-09 07:05 +0200
    Re: gruppi Giorgio Bibbiani <giorgiobibbiani@tin.it> - 2025-06-08 21:22 +0200

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