Discrete Mathematics..

288 Matrix Algebra6.2 Some Special MatricesIt is convenient to distinguish several different ‘families’ of matrices. A list ofthese together with their defining characteristics is given below.A square matrix is one having the same number of rows as it has columns. Thefollowing are examples of square matrices:( 2 3−1 4)⎛⎝ 3 2 0 ⎞4 5 −1 ⎠ .2 −3 7A column matrix (or column vector) is a matrix having only one column.Examples are:⎛ ⎞( )−12 ⎜ 4⎟1 ⎝ 2 ⎠ .10A row matrix (or row vector) is a matrix having only one row, for example:( ) ( ) 7 1 −2 3 2 1 0 −1 .Row and column vectors are often (but not always) denoted by lower-case boldletters. In handwriting, lower case letters with a line or tilde underneath (theprinter’s notation for bold print) are used. Thus we may write:u = ( 2 4 3 −6 ) or ũ = ( 2 4 3 −6 ) .A row vector is sometimes written with its elements separated by commas, forexample u = (2, 4, 6, −2, 2).A zero matrix (or null matrix) is one where every element is zero. So for a zeromatrix A, a ij = 0 for all values of i and j. Since different zero matrices existfor every possible dimension it is usual to denote a zero matrix by O m×n wherem × n is the dimension of the matrix. For example,O 2×3 =( 0 0 00 0 0)and O 2×2 =( 0 00 0A diagonal matrix is a square matrix where all of the elements are zero exceptpossibly those occupying the positions diagonally from the top-left corner to thebottom right corner. In any square matrix, these elements constitute what is).