1.4.1 Arrays: vectors and matrices

In the last exercise, you were introduced to arrays. Type, c and you will see that it is a row vector with three elements. A vector is a one-dimensional array. Now, type d. d is a vector as well but a column vector. Use the size command to see the ``size'' and ``shape'' of an array. Try, size(c). We see that c is an array with one row and 3 columns, a $1\times3$ array. (For one-dimensional arrays, length also works.) Try size(d). size tells us that d is a $4\times1$ array, that is, an array with 4 rows and one column. If you followed that, it shouldn't be surprising that f is a $2\times2$ array. Note that all this information is also available using the whos command (or in the Workspace window if it visible). Arrays are entered by listing the elements in between square brackets $[\dots]$. Elements in a single row are separated by commas and individual columns are separated by semicolons (look at the example above again). To make sure that you understand this, try making two vectors, one column vector and one row vector. Verify that you've done it correctly by using the whos command. Entering arrays and matrices can be made easier by entering them ``visually,'' rather than trying to keep track of all of the commas and semicolons. Separate individual elements in a row by spaces and individual rows by a carriage return (that's ``old-timer speak'' for hitting the return key). For example, try this:

rvec = [1 2 3]
cvec = [4
        3
        4
        2]
mat1 = [3 3 4
        4 5 6
        9 9 0]

Note that you don't to have line up all the columns. This works just as well:

rvec = [1 2 3]
cvec = [4
   3
   4
   2]
mat1 = [3 3 4
   4 5 6
   9 9 0]

Another slick way of defining the values of a one-dimensional array, a vector, is by using the colon notation. We can define an array containing the numbers 1-10 by t=[1:10] (Try it.) To go by twos, try t=[1:2:10] To go by halves, try t=[1:.5:10]. You could also get all the numbers between 1 and 1000, inclusive, with t=[1:1000]. Try it and you will see that we need to learn how to define arrays without MATLAB parroting back to us each value (especially if more is on). Make MATLAB talk quietly using a semicolon to end a command. Try, r=[0:.1:pi];. You can verify that MATLAB really did assign 32 values to the array r by just typing r at the command line. (Do it.)