Working with Matrices (Getting Started)

Getting Started with MATLAB

This section introduces you to other ways of creating matrices.

MATLAB provides four functions that generate basic matrices:


`zeros`	All zeros
`ones`	All ones
`rand`	Uniformly distributed random elements
`randn`	Normally distributed random elements

Some examples:

Z = zeros(2,4)
Z =
     0     0     0     0
     0     0     0     0

F = 5*ones(3,3)
F =
     5     5     5
     5     5     5
     5     5     5

N = fix(10*rand(1,10))
N =
     4     9     4     4     8     5     2     6     8     0

R = randn(4,4)
R =
    1.0668    0.2944   -0.6918   -1.4410
    0.0593   -1.3362    0.8580    0.5711
   -0.0956    0.7143    1.2540   -0.3999
   -0.8323    1.6236   -1.5937    0.6900

load

The load command reads binary files containing matrices generated by earlier MATLAB sessions, or reads text files containing numeric data. The text file should be organized as a rectangular table of numbers, separated by blanks, with one row per line, and an equal number of elements in each row. For example, outside of MATLAB, create a text file containing these four lines:

    16.0     3.0     2.0    13.0
     5.0    10.0    11.0     8.0
     9.0     6.0     7.0    12.0
     4.0    15.0    14.0     1.0

Store the file under the name magik.dat. Then the command

load magik.dat

reads the file and creates a variable, magik, containing our example matrix.

M-Files

You can create your own matrices using M-files, which are text files containing MATLAB code. Just create a file containing the same statements you would type at the MATLAB command line. Save the file under a name that ends in .m.

NOTE
To access a text editor on a PC or Mac, choose Open or New from the File menu or press the appropriate button on the toolbar. To access a text editor under UNIX, use the ! symbol followed by whatever command you would ordinarily use at your operating system prompt.

For example, create a file containing these five lines:

    A = [ ...
    16.0     3.0     2.0    13.0
     5.0    10.0    11.0     8.0
     9.0     6.0     7.0    12.0
     4.0    15.0    14.0     1.0 ];

Store the file under the name magik.m. Then the statement

magik

reads the file and creates a variable, A, containing our example matrix.

Concatenation

Concatenation is the process of joining small matrices to make bigger ones. In fact, you made your first matrix by concatenating its individual elements. The pair of square brackets, [], is the concatenation operator. For an example, start with the 4-by-4 magic square, A, and form

B = [A  A+32; A+48  A+16]

The result is an 8-by-8 matrix, obtained by joining the four submatrices.

B =

    16     3     2    13    48    35    34    45
     5    10    11     8    37    42    43    40
     9     6     7    12    41    38    39    44
     4    15    14     1    36    47    46    33
    64    51    50    61    32    19    18    29
    53    58    59    56    21    26    27    24
    57    54    55    60    25    22    23    28
    52    63    62    49    20    31    30    17

This matrix is half way to being another magic square. Its elements are a rearrangement of the integers 1:64. Its column sums are the correct value for an 8-by-8 magic square.

sum(B)

ans =
   260   260   260   260   260   260   260   260

But its row sums, sum(B')', are not all the same. Further manipulation is necessary to make this a valid 8-by-8 magic square.

Deleting Rows and Columns

You can delete rows and columns from a matrix using just a pair of square brackets. Start with

X = A;

Then, to delete the second column of X, use

X(:,2) = []

This changes X to

X =
    16     2    13
     5    11     8 
     9     7    12
     4    14     1

If you delete a single element from a matrix, the result isn't a matrix anymore. So, expressions like

X(1,2) = []

result in an error. However, using a single subscript deletes a single element, or sequence of elements, and reshapes the remaining elements into a row vector. So

X(2:2:10) = []

results in

X =
    16     9     2     7    13    12     1

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