MATLAB works with essentially only one kind of object-a rectangular numerical matrix with possibly complex entries; all variables represent matrices. In some situations, 1-by-1 matrices are interpreted as scalars and matrices with only one row or one column are interpreted as vectors.
Matrices can be introduced into MATLAB in several different ways:
A = [1 2 3; 4 5 6; 7 8 9]and
A = [ 1 2 3 4 5 6 7 8 9 ]creates the obvious 3-by-3 matrix and assigns it to a variable A . Try it. The elements within a row of a matrix may be separated by commas as well as a blank.
When listing a number in exponential form (e.g. 2.34e-9), blank spaces must be avoided. Listing entries of a large matrix is best done in an M-file, where errors can be easily edited away (see sections 12 and 14).
The built-in functions rand, magic, and hilb, for example, provide an easy way to create matrices with which to experiment. The command rand(n) will create an n x n matrix with randomly generated entries distributed uniformly between 0 and 1, while rand(m,n) will create an m x n one. magic(n) will create an integral n x n matrix which is a magic square (rows and columns have common sum); hilb(n) will create the n x n Hilbert matrix, the king of ill-conditioned matrices ( m and n denote, of course, positive integers). Matrices can also be generated with a for-loop (see section 6 below).
Individual matrix and vector entries can be referenced with indices inside parentheses in the usual manner. For example, A(2,3) denotes the entry in the second row, third column of matrix A and x(3) denotes the third coordinate of vector x. Try it. A matrix or a vector will only accept positive integers as indices.