## Thursday, August 02, 2018

### Dialectic of Linear Algebra -- ‘Dialectogram’: ‘A Systematic-Dialectic Method of Presentation for the Domain of the Linear-Algebraic Mathematical Objects’.

Dialectic of Linear Algebra --

Dialectogram:A Systematic-Dialectic Method of Presentation for the Domain of the Linear-Algebraic Mathematical Objects.

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