How Matrices Began...




The beginning of matrices goes back to the second century BC although traces can be seen back all the way to the fourth century BC. However, it was not until the end of the 17th Century that the matrix ideas reappeared and development really began to progress.

It is not surprising that the beginning of matrices should arise through the study involving systems of linear equations , because matrices help in the solutions of these equations.

The Babylonians first started studying the problems that lead to simultaneous linear equations and some of these problems are preserved in clay tablets that survived to present day.The Chinese, between 200 BC and 100 BC, came much closer to matrices than the Babylonians. Indeed it is fair to say that the text Nine Chapters of the Mathematical Art written during the Han Dynasty gives the first known example of matrix methods.

One method would include what is now known as the Gaussian Elimination (which is a method used to solve linear equations). Albeit, this method of elimination would not become popular to mathematicians until the early 19th Century.

The matrix theory was the result of a fifty-year study done by a man named Leibniz who studied coefficient systems of quadratic forms. Many common manipulations of the uncomplicated matrix theory appeared long before matrices were the object of mathematical investigation.

Gauss first started to describe matrix multiplication (which he thinks of as an organization of numbers, so he had not yet reached the concept of matrix algebra) and the INVERSE OF A MATRIX in the particular context of the collection of coefficients of quadratic forms.

Gaussian elimination first appeared in the text Nine Chapters of the Mathematical Art written in 200 BC by Gauss during his work in the study of the asteroid Pallas. Using observations of Pallas taken between 1803 and 1809, Gauss obtained a system of six linear equations in six unknowns. Gauss gave a systematic method for solving such equations, which is precisely Gaussian elimination on the coefficient matrix. The MULTIPLICATION THEORM is proven and published for the first time in an 1812 paper.

Eisenstein, in 1844, denoted linear substitutions by a single letter and showed how to ADD ADD and multiply them like ordinary numbers. It is rational to state that Eisenstein was the first to think of linear substitutions.

The first person to use the term 'matrix' was Sylvester in 1850. Sylvester defined a MATRIX to be an oblong arrangement of terms and saw it as something that led to various determinants from square assortment contained within it.

In 1853 a man named Cayley published a note giving, for the first time, the inverse of a matrix. Cayley defined the matrix algebraically using addition, multiplication, scalar multiplication and inverses. He gave a precise explanation of an inverse of a matrix. After using addition, multiplication and inverses with matrices, SUBTRACTION and division were soon to follow...

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Latest update to this document: 16 November 2001

Jessica Schneider: jeschnei@nmu.edu