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

Other articles related to "history":

Spain - History - Fall of Muslim Rule and Unification
... The breakup of Al-Andalus into the competing taifa kingdoms helped the long embattled Iberian Christian kingdoms gain the initiative ... The capture of the strategically central city of Toledo in 1085 marked a significant shift in the balance of power in favour of the Christian kingdoms ...
Xia Dynasty - Modern Skepticism
... The Skeptical School of early Chinese history, started by Gu Jiegang in the 1920s, was the first group of scholars within China to seriously question the traditional story of its early history "the later the ... early Chinese history is a tale told and retold for generations, during which new elements were added to the front end" ...
History of Computing
... The history of computing is longer than the history of computing hardware and modern computing technology and includes the history of methods intended for pen and paper or for chalk and slate, with or ...
Voltaire - Works - Historical
... History of Charles XII, King of Sweden (1731) The Age of Louis XIV (1751) The Age of Louis XV (1746–1752) Annals of the Empire – Charlemagne, A.D ... the Manners of Nations (or 'Universal History') (1756) History of the Russian Empire Under Peter the Great (Vol ... II 1763) History of the Parliament of Paris (1769) ...
Casino - History of Gambling Houses
... has been seen in almost every society in history ... Greeks and Romans to Napoleon's France and Elizabethan England, much of history is filled with stories of entertainment based on games of chance ... In American history, early gambling establishments were known as saloons ...

Famous quotes containing the word history:

    You that would judge me do not judge alone
    This book or that, come to this hallowed place
    Where my friends’ portraits hang and look thereon;
    Ireland’s history in their lineaments trace;
    Think where man’s glory most begins and ends
    And say my glory was I had such friends.
    William Butler Yeats (1865–1939)

    the future is simply nothing at all. Nothing has happened to the present by becoming past except that fresh slices of existence have been added to the total history of the world. The past is thus as real as the present.
    Charlie Dunbar Broad (1887–1971)

    ... all big changes in human history have been arrived at slowly and through many compromises.
    Eleanor Roosevelt (1884–1962)