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.
Read more about this topic: Linear Function
Famous quotes containing the word spaces:
“Though there were numerous vessels at this great distance in the horizon on every side, yet the vast spaces between them, like the spaces between the stars,—far as they were distant from us, so were they from one another,—nay, some were twice as far from each other as from us,—impressed us with a sense of the immensity of the ocean, the “unfruitful ocean,” as it has been called, and we could see what proportion man and his works bear to the globe.”
—Henry David Thoreau (1817–1862)