Determinants

The Chinese method of representing the coefficients of the unknowns of several linear equations by using rods on a calculating board led to the discovery of determinants. Two thousand years ago, the Chinese used this method to solve simultaneous equations, which is now known as Cramer’s rule.

The Japanese mathematician Seki Kowa is credited with the discovery of determinants in 1683. He used his method of solving simultaneous equations to find the roots of an equation. The German mathematician G.W. Leibniz also discovered determinants in 1693, and his work contains the expansion of a determinant.

In 1750, Cramer presented a rule for solving simultaneous equations, now known as Cramer’s Rule. However, this rule was likely known to Maclaurin as early as 1729.

The theory of determinants was further developed by Lagrange in 1773. He studied general determinants of the second and third order and applied them to questions of elimination.

In 1801, Gauss used determinants in his theory of numbers. The term ‘determinant’ was first introduced by him, though not in its present sense.

Cauchy was the first to use the term ‘determinant’ in its modern sense. He was the first to prove the general theorem on the multiplication of determinants and made significant contributions to the theory of determinants.

Jacobi also made important contributions to the theory of determinants. In 1841, he gave the general principles of determinants and introduced the functional determinant, which is now known as the Jacobian determinant.