## Matrix Algebra: Introduction

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra.

In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra.

Here is the first topic where we define a matrix, vector, submatrix, square matrix, triangular matrix (upper and lower), diagonal matrix, identity matrix, and diagonally dominant matrix.  Get the information in form of textbook content, lecture videos, multiple choice test, problem set and PowerPoint presentation.

Introduction

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## MATLAB code for bubble sort

In the previous blog, we spelled out the bubble sort algorithm for putting an array of numbers in an ascending order.   In this post, I am posting the matlab program. It is better to download the program as single quotes in the pasted version do not translate properly when pasted into a mfile editor of MATLAB or see the html version for clarity and sample output.

%% PUTTING AN VECTOR OF NUMBERS IN AN ASCENDING ORDER?
% Language : Matlab 2007a
% Authors : Autar Kaw
% Last Revised : November 8, 2009
% Abstract: This program shows you how to put a vector
% of numbers in an ascending order using the bubble sort method
clc
clear all
disp(‘This program shows the bubble sort method’)
disp(‘to put a vector of numbers in an ‘)
disp(‘ascending order’)
disp(‘Matlab 2007a’)
disp(‘Authors : Autar Kaw’)
disp(‘Last Revised : November 8, 2009’)
disp(‘http://numericalmethods.eng.usf.edu&#8217;)
disp(‘  ‘)
%% INPUTS
% The vector of numbers
disp (‘INPUTS’)
disp(‘Input the vector of numbers’)
A=[18  7  6  15  4  13];
disp(A)
%% SOLUTION
% Number of entries, n
n=length(A);
% making (n-1) passes
for j=1:1:n-1
% comparing each number with the next and swapping
for i=1:1:n-1
if A(i)>A(i+1);
% temp is a variable where the numbers are kept
% temporarily for the switch
temp=A(i);
A(i)=A(i+1);
A(i+1)=temp;
end
end
end

%% OUTPUT
disp(‘  ‘)
disp (‘OUTPUT’)
disp (‘The ascending matrix is’)
disp(A)

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This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu, the textbook on Numerical Methods with Applications available from the lulu storefront, and the YouTube video lectures available at http://numericalmethods.eng.usf.edu/videos and http://www.youtube.com/numericalmethodsguy