Standardlinjär

Standardlinjär is a term found in Swedish mathematical and applied literature that translates roughly to "standard linear." It does not refer to a single, universally defined object; its exact meaning depends on the disciplinary context.

In linear algebra, standardlinjär commonly denotes the representation of a linear transformation with respect to the standard basis. If T: V → W is a linear map between finite-dimensional vector spaces over a field, its standard matrix A is defined by A x = T(x) for coordinate vectors x in the chosen bases. The matrix A is said to be the standard matrix or the standard linear form of T. Computations such as solving for x given Ax = b are performed in these standard coordinates.

In applied fields, the term may be used to refer to a canonical linear model or operator within that domain. For example, in numerical analysis, a standard linear system refers to a system of linear equations Ax = b with A as the coefficient matrix; in computer graphics, standard linear transformations include operations like rotation, scaling, and projection expressed as matrices in the standard basis.

Because the phrase is not rigidly codified, precise interpretation should be taken from the surrounding text. When encountered, readers should identify the specific vector spaces, bases, and matrices involved to determine the exact meaning of standardlinjär in that context.

See also: linear transformation, matrix, basis, canonical form, ordinary least squares (in statistics), linear system.