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Matrix Definition in Math

Matrix Definition in Math Introduction:
While solving linear systems of equations, a new notation was introduced to reduce the amount of writing. For this new notation, the word matrix was first used by the English mathematician James Sylvester (1814 – 1897). Arthur Cayley (1821 – 1895) developed the theory of matrices and used them in linear transformations. Nowadays, matrices are
used in high-speed computers and also in other various disciplines.
The concept of determinants was used by Chinese and Japanese but the Japanese mathematician Seki Kowa (1642 – 1708) and the German mathematician Gottfried Wilhelm Leibniz (1646 – 1716) is credited for the invention of determinants. G. Cramer (1704 – 1752) applied the determinants successfully for solving the systems of linear equations.

Matrix definition: A rectangular array of numbers enclosed by a pair of brackets such as:

is called matrix.

The horizontal lines of numbers are called rows and the vertical lines of numbers are called columns. The numbers used in rows or columns are said to be the entries or elements of the matrix.
The matrix in (i) has two rows and three columns while the matrix in (ii) has 4 rows and three columns. Note that the number of elements of the matrix in (ii) is 4\times 3= 12. Now we give a general definition of a matrix.

Generally, a bracketed rectangular array of m\times n elements
aij (i = 1, 2, 3, …., m; j = 1, 2, 3, …., n), arranged in m rows and n columns such as:

Matrix Definition

is called an m by n matrix (written as m\times n matrix).
m\times n is called the order of the matrix in (iii) .

We usually use capital letters such as A, B, C, X, Y, etc., to represent the matrices and small letters such as a, b, c,…, m, n,…, a_{11}, a_{12}, a_{13} …., etc., to indicate the entries of the matrices.
Let the matrix in (iii) be denoted by A. The ith row and the jth column of A are indicated
in the following tabular representation of A.

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