UUniniveversrsiitty of Hy of Haawwaaiiii  
           ICS141:  
           Discrete Mathematics for 
           Computer Science I 
                Dept. Information & Computer Sci., University of Hawaii 
                                               
                                       Jan Stelovsky 
                         based on slides by Dr. Baek and Dr. Still 
                     Originals by Dr. M. P. Frank and Dr. J.L. Gross 
                                 Provided by McGraw-Hill  
  ICS 141: Discrete Mathematics I – Fall 2011                                        13-1 
                                                                                   UUniniveversrsiitty of Hy of Haawwaaiiii  
            Lecture 19 
            Chapter 3. The Fundamentals 
                     3.8 Matrices 
             
   ICS 141: Discrete Mathematics I – Fall 2011                                         13-2 
                    3.8 Matrices                                                                                                   UUniniveversrsiitty of Hy of Haawwaaiiii  
             n   A matrix is a rectangular array of 
                  objects (usually numbers).                                                                      2           3
                                                                                                                ⎡               ⎤
                                                                                                                ⎢               ⎥
             n   An m × n (“m by n”) matrix has                                                                  5 −1
                  exactly m horizontal rows, and n                                                              ⎢               ⎥
                                                                                                                ⎢7           0⎥
                  vertical columns.                                                                             ⎣               ⎦
                                                                                                           A 3×2 matrix 
             n   Plural of matrix = matrices (say MAY-trih-sees) 
             n   An n × n matrix is called a square matrix 
    ICS 141: Discrete Mathematics I – Fall 2011                                                                                          13-3 
                    Applications of Matrices                                                                                       UUniniveversrsiitty of Hy of Haawwaaiiii  
                    n   Tons of applications, including: 
                           n  Solving systems of linear equations 
                           n  Computer Graphics, Image Processing 
                           n  Games 
                           n  Models within many areas of  
                                Computational Science & Engineering 
                           n  Quantum Mechanics, Quantum Computing 
                           n  Many, many more… 
    ICS 141: Discrete Mathematics I – Fall 2011                                                                                          13-4