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:

- Entered by an explicit list of elements,
- Generated by built-in statements and functions,
- Created in M-files (see sections 12 and 14 below),
- Loaded from external data files (see User's Guide).

andA = [1 2 3; 4 5 6; 7 8 9]

creates the obvious 3-by-3 matrix and assigns it to a variableA = [ 1 2 3 4 5 6 7 8 9 ]

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.

Wed Mar 13 19:15:55 MET 1996