The Living Thing / Notebooks :

Differential geometry, geometric algebra etc

TBD. A pragmatic guide to manifold wrangling, whatever your formalism.

Key words: Clifford algebra, differential forms…

See also information geometry.


Clifford Algebra formalism

Hestenes’ school.

Handy texts:

Alan Bromborsky, An introduction to Geometric Algebra and Calculus

Alan Macdonald, Geometric Algebra:

Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas, including linear algebra, multivariable calculus, real analysis, complex analysis, and euclidean, noneuclidean, and projective geometry. They provide a unified mathematical language for physics (classical and quantum mechanics, electrodynamics, relativity), the geometrical aspects of computer science (e.g., graphics, robotics, computer vision), and engineering.

Differential forms formalism

How is tensor?

Multilinear weirdness.