Matrix Algebra review - Matrices 1 Matrix Algebra Matrix...

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Matrices 1. Matrix Algebra Matrix algebra. Previously we calculated the determinants of square arrays of numbers. Such arrays are important in mathematics and its applications; they are called matrices . In general, they need not be square, only rectangular. A rectangular array of numbers having m rows and n columns is called an m × n matrix . The number in the i -th row and j -th column (where 1 - i - m, 1 - j - n ) is called the ij-entry , and denoted a ij ; the matrix itself is denoted by A , or sometimes by ( a ij ). Two matrices of the same size are equal if corresponding entries are equal. Two special kinds of matrices are the row-vectors : the 1 × - n matrices ( a 1 , a 2 , . . . , a n ); and the column vectors : the m × - 1 matrices consisting of a column of m numbers. From now on, row-vectors or column-vectors will be indicated by boldface small letters; when writing them by hand, put an arrow over the symbol. Matrix operations There are four basic operations which produce new matrices from old.
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