STEER Program Notes
MATLAB allows for easy manipulation of matrices. The following is an interesting take on inverses of matrices that I found in the MATLAB demo programs.
(In MATLAB programs, a “%” symbol indicates a comment.)
n = 100;
a = rand(n); %Creates nxn matrix "a" containing random values from 0 to 1.
imagesc(a); %Scales the data in "a" and displays it as an image.
%Each element in "a" corresponds to a rectangular
%area in the image. The values of the elements of
%"a" are indices into the current colormap that
%determine the color of each patch.
colormap(hot); %A colormap is an m x 3 matrix of real numbers
%between 0.0 and 1.0. Each row is an RGB vector
%that defines one color. "hot" is a colormap that
%varies smoothly from black, through shades of red,
%orange, and yellow, to white.
axis square; %Makes the current axis square. The x and y axis are
%equal lengths and the increments are equal.
b = inv(a); %Creates the inverse matrix of "a".
imagesc(b); %See above.
axis square; %See above.
imagesc(a * b); %Creates the image of the matrix of a * b.
axis square; %Creates a square plot. Since this should be the
%identity matrix, one should expect the graph to be
%a white line down the diagonal of the matrix,
%representing the ones down the diagonal.
%All else should be black (zeroes).
Plotting Graphs in MATLAB - One can also easily plot graphs and sets of graphs in MATLAB. This allows for simultaneous comparisons of functions.
%Create a vector of values from 0 to 5, in steps of .5
t = 0:.5:5;
%Create a 2x1 set of graphs. This is the first of two graphs.
%Plot t vs. sin(t).
subplot (2,1,1); plot(t,sin(t));
%Repeat for cos(t). This is the second of 2 graphs.
subplot (2,1,2); plot(t,cos(t));