Linear Algebra - History

History

The study of linear algebra and matrices first emerged from the study of determinants, which were used to solve systems of linear equations. Determinants were used by Leibniz in 1693, and subsequently, Gabriel Cramer devised Cramer's Rule for solving linear systems in 1750. Later, Gauss further developed the theory of solving linear systems by using Gaussian elimination, which was initially listed as an advancement in geodesy.

The study of matrix algebra first emerged in England in the mid 1800s. In 1848, James Joseph Sylvester introduced the term matrix, which is Latin for "womb". While studying compositions of linear transformations, Arthur Cayley was led to define matrix multiplication and inverses. Crucially, Cayley used a single letter to denote a matrix, thus treating a matrix as an aggregate object. He also realized the connection between matrices and determinants, and wrote "There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants".

The first modern and more precise definition of a vector space was introduced by Peano in 1888; by 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged. Linear algebra first took its modern form in the first half of the twentieth century, when many ideas and methods of previous centuries were generalized as abstract algebra. The use of matrices in quantum mechanics, special relativity, and statistics helped spread the subject of linear algebra beyond pure mathematics. The development of computers led to increased research in efficient algorithms for Gaussian elimination and matrix decompositions, and linear algebra became an essential tool for modelling and simulations.

The origin of many of these ideas is discussed in the articles on determinants and Gaussian elimination.

Recently, Sinologist Roger Hart argued Chinese mathematicians found a method "essentially equivalent to the solution of systems of N equations in N unknowns in modern algebra" a millennium before the West.

Read more about this topic:  Linear Algebra

Famous quotes containing the word history:

    The history of all countries shows that the working class exclusively by its own effort is able to develop only trade-union consciousness.
    Vladimir Ilyich Lenin (1870–1924)

    ... in America ... children are instructed in the virtues of the system they live under, as though history had achieved a happy ending in American civics.
    Mary McCarthy (1912–1989)

    The true theater of history is therefore the temperate zone.
    Georg Wilhelm Friedrich Hegel (1770–1831)