Euler introduced the term affine (Latin affinis, "related") in 1748 in his book "Introductio in analysin infinitorum."
Felix Klein's Erlangen program recognized affine geometry as a generalization of Euclidean geometry.
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An affine combination is a linear combination of vectors in Euclidian space in which the coefficients add up to one.
View all Sir William Rowan Hamilton invented the linear equation in 1843.
The history of modern linear algebra dates back to the early 1840's. In 1843, William Rowan Hamilton introduced quaternions, which describe mechanics in three-dimensional space. In 1844, Hermann Grassmann published his book Die lineale Ausdehnungslehre (see References). Arthur Cayley introduced matrices, one of the most fundamental linear algebraic ideas, in 1857. Despite these early developments, linear algebra has been developed primarily in the twentieth century.
dual space W* of W can naturally identified with linear functionals
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