Linear Function - Vector Spaces

Vector Spaces

In advanced mathematics, a linear function means a function that is a linear map, that is, a map between two vector spaces that preserves vector addition and scalar multiplication. For example, if and are represented as coordinate vectors, then the linear functions are those functions that can be expressed as

where M is a matrix. A function

is a linear map if and only if = 0. For other values of this falls in the more general class of affine maps.

Linear functions form the basis of linear algebra.

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Famous quotes containing the word spaces:

    “Le silence éternel de ces espaces infinis m’effraie. The eternal silence of these infinite spaces frightens me.”
    —Blaise Pascal (1623–1662)