The first matrix is mentioned in ancient China, called then the "magic square". The main application of matrix was the solution of linear equations. A little later "magic square" is mentioned by the Arab mathematicians, then appeared the principle of addition of matrices.
After the development of the theory of determinants in the late 17th century, Gabriel Cramer began to develop his theory in the 18th century and published "Cramer's rule" in 1751. Around the same time period has appeared "Gauss elimination".
Matrix theory came into existence in the middle of the XIX century in the works of William Hamilton and Arthur Cayley. Fundamental results in the theory of matrices belong to Karl Weierstrass, Ferdinand Georg Frobenius and Marie Ennemond Camille Jordan. The modern name "matrix" was introduced by James Joseph Sylvester in 1850.
Applying of matrix
Matrices are widely used in mathematics and physics for a compact recording and solving systems of linear algebraic equations and systems of differential equations. The number of rows corresponds to the number of equations and the number of columns corresponds to the number of unknown quantities. The matrices can significantly simplify the solution systems of linear equations by reducing it to the operations on matrices.
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