{"id":5136,"date":"2014-04-17T06:05:52","date_gmt":"2014-04-16T21:05:52","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=5136"},"modified":"2014-08-01T18:36:36","modified_gmt":"2014-08-01T09:36:36","slug":"definition-of-a-matrix","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5136","title":{"rendered":"Definition of a matrix"},"content":{"rendered":"
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A matrix of order m × n<\/em>, or m by n matrix<\/em>, is a rectangular array of numbers having m<\/em> rows and n<\/em> columns. It can be written in the form <\/p>\n

A = \\left( \\begin{array}{ccccc} a_{11} & a_{12} & a_{13} & \\cdots & a_{1n} \\\\ a_{21} & a_{22} & a_{23} & \\cdots & a_{2n} \\\\ \\cdots & \\cdots & \\cdots & \\cdots & \\cdots \\\\ a_{m1} & a_{m2} & a_{3m} & \\cdots & a_{mn} \\end{array} \\right)\\cdots(1)<\/p>\n

Each number a_{jk} in this matrix is called an element<\/em>. The subscripts j and k indicate respectively the row and column of the matrix in which the element appears. <\/p>\n

We shall often denote a matrix by a letter, such as A in (1), or by the symbol (a_{jk}) which shows a representative element. <\/p>\n

A matrix having only one row is called a row matrix<\/em> or row vector<\/em> while a matrix having only one column is called a column matrix<\/em> or column vector<\/em>. If the number of rows m and columns n are equal the matrix is called a square matrix<\/em> of order n \\times n or briefly n. A matrix is said to be a real matrix<\/em> or complex matrix<\/em> according as its elements are real or complex numbers. <\/p>\n<\/blockquote>\n