This portion of my web-space is in a state of flux (since 1997/Spring) while I dismantle a huge page, add in some related fragments from other pages and set the pieces together in such good order as I can manage, while at the same time adjusting to many notational choices I've made since I wrote on this topic before.

Thus far, I here describe:

- addition's
- place in the sun, some context and scalars.
- rationals
- and the continuum
- The one-dimensional special case
- which has its simplifications, yet shouldn't be over-simplified.
- positivity
- the consequences of not having an additive identity,
- tensors, transposition and trace
- three fundamental operations in linear algebra; the page on the second now covers much of what the other two cover.
- the complex numbers
- and their representation by a sphere.
- hermitian
- conjugation combined with transposition, consequent symmetries and the two-dimensional special case.
- Quadratic forms
- which provide, among other things, a way to encode a notion of length via a metric.
- rotations
- a particular class of isometry, preserving the lengths of a given metric.
- unitary
- transformations associated with hermitian forms; the example of SU(2)
- projection
- the properties of self-square linear maps – i.e., linear (V|f:V) for which f·f=f,
- projectors
- which are projections whose composite with some metric-tensor is symmetric,
- alternating algebra
- which weaves antisymmetry into the world of smooth manifolds and provides the basis for Hodge duality.
- Lagrange's multipliers
- A method for optimising functions of many variables, subject to constraints.
- Euclidean spaces
- the classical flat world and its relationship to linearity
- Differentiation
- introduced as naturally arising in the general linear context (in preference to arising for scalars and being induced thereby for linear contexts).
- ramblings
- sketches towards a better approach, originally from my newer area
- and an old page on linearity,
- which I'm shredding along with one on scalars. Other old cruft include: mappings, binary operators