Linear Algebra

A section of Algebra that deals with vectors and matrices.

See: LinearAlgebraVsNumericalAnalysis MatrixAnalysis

The above definition is somewhat misleading; although in practice I suppose that most people view it this way. If anyone cares, it would perhaps be more accurate to say that 'Linear Algebra' is the study of the algebra of linear transformations. Most elementary linear algebra does indeed involve linear transformations between inner product or vector spaces on the real/complex Field (i.e. 'vectors and matrices') but there is a lot of power in more abstraction (and matrices are more a notational convenience than an object of study)...

For more depth, see http://en.wikipedia.org/wiki/Linear_algebra.
An important part of LinearAlgebra is actually concerned with things like FunctionSpaces?, which are infinite-dimensional and thus difficult to represent in a computer. Crud...by saying too much I may sound fringe. I am merely appealing to (1) modern topology, all 3 branches, and (2) its known applicability to other math. fields. I do not claim anything beyond that, but that in itself is huge, and not that widely known.

CategoryTheory treats these issues more simply, but I am still a novice in that better approach to things; CategoryTheory is appealing because it seems to make so very much simple, with morphism diagrams, similarly to how Feynman diagram simplified particle interactions. -- DougMerritt
Linear systems in general are those with two operations, call them function F and operator '*', such that: LinearAlgebra addresses the basics of some such systems, but that basic issue of "linearity" is vastly larger and pervades many branches of pure and applied math. There are relatively few branches of mathematics where linearity has no importance. -- DougMerritt


See LinearAlgebraPackage (LAPACK) for information about implementing LinearAlgebra in FortranLanguage or CeePlusPlus.

See also GeometricalVectors AffineTransformation LinearTransformation
CategoryMath

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