Dialectic of Linear Algebra --
‘Dialectogram’:
‘A Systematic-Dialectic Method of Presentation for the Domain of the Linear-Algebraic Mathematical Idea-Objects’.
Dear
Reader,
The case of the Domain
of the ‘‘‘mathematical objects’’’ central to standard Linear Algebra, as
treated in this blog entry -- the Domain
of arrays, matrices, vectors, and scalars -- can serve as yet another example
of the failure of the contemporary mathematical sub-culture to recognize the «aufheben» ‘dialecticality’ of its primary thought-products,
already latent and unconsciously present in its history, and in its present-day
proofs as well.
The Octadic, mixed-format ‘dialectograms’
below describe, in
systematic order -- in consecutive, simplest to more complex order -- these
categories of mathematical objects that are central to contemporary Linear
Algebra, & which may form part of a systematic, dialectical categorial-progression
method of presentation of the contemporary Domain
of “Standard” Linear Algebra.
To convey the dialectical -- or «aufheben» -- architectonic of these mathematical objects
in the most direct way, we will here simply say that --
- Each typical [1-D] vector is a vertical or horizontal “stack” or “deck” of scalars -- a ‘meta-scalar’, each one made up out of a diverse multiplicity of scalars;
- Each typical [2-D] matrix is a vertical or horizontal “stack” or “deck” of vectors -- a ‘meta-vector’, each one made up out of a diverse multiplicity of vectors; it is also a ‘meta-meta-scalar’, or ‘meta2-scalar’;
- Each typical [3-D] array is a vertical or horizontal “stack” or “deck” of matrices -- a ‘meta-matrix’, each one made up out of a diverse multiplicity of matrices; it is also a ‘meta-meta-meta-scalar’, or ‘meta3-scalar’, and a ‘meta-meta-vector’, or ‘meta2-vector’ .
FYI: Much of the work
of Karl Seldon, and of his collaborators, including work by “yours truly”, is
available for your
free-of-charge download via --
Regards,
Miguel Detonacciones,
Member, Foundation Encyclopedia Dialectica
[F.E.D.],
Officer, F.E.D.
Office of Public Liaison
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