Matricial derivations

A teenager idea.

Go to the “Table of contents”.

Title : PERIAT, T.: Matricial derivations, ISBN 978-2-36923-015-1, EAN 9782369230151, 21 march 2021, 25 + 12 pages (part 01 and 02).

Documents :

  • Part 01: Isbn 015 1 matricial derivation v1 1Isbn 015 1 matricial derivation v1 1 (268.23 Ko), 25 pages.

 

 

 

  • Part 02: Isbn 015 1 gb 20210320 part 02Isbn 015 1 gb 20210320 part 02 (310.73 Ko), 12 pages.

 

 

Comments:

You sometimes have asked yourself if there exists a mathematical tool supplanting the rules that your memory must store to realize diverse derivations on numerical functions or/and -why not- on vector fields. The concept of matricial derivation is a pragmatic answer to that questioning.

This memoir (in two parts) introduces the concept in staying at an intuitive and formal level, lying the basic stones for further future explorations.

A matricial derivation delegates the role normally played by a set of rules acting on numerical functions (e.g.: (sin x)'x = cos x) to a set of matrices acting on elements in a vector space.

The deformed tensor products and their diverse decompositions, especially the trivial ones, are the guiding common threads illustrating this concept.

The progression explains the indirect link with the (E) question.

To go further: “The Tartaglia-Cardan method”.

Go back to the page: “Mathematical tools”.

© Thierry PERIAT

Last edited: 15/09/2021