14.2.4  Creating a matrix with a formula or function

Use a function or a formula to specify the elements of a matrix with the makemat or matrix command.

• makemat takes three arguments:
  • f, a function of two variables j and k which returns the value of a_j,k, the element at row index j and column index k of the resulting matrix.
  • n and p, two positive integers.
• makemat(f,n,p) returns the n× p matrix A=[a_jk] with a_jk=f(j,k) for j=1…,n and k=1,…,p.

The matrix command can be used similarly, but note that the arguments are given in a different order and the indices start at 1. (See Section 14.4.2 for other uses of matrix.)

• matrix takes two mandatory arguments and one optional argument:
  • n and p, two integers.
  • Optionally, f, a function of two variables j and k which should return the value of a_j,k, the element at row index j and column index k of the resulting matrix.
• matrix(n,p) returns the n× p matrix consisting of all zeros.
• matrix(n,p,f) returns the n× p matrix A=[a_jk] with a_jk=f(j,k) for j=1,…,n and k=1,…,p.

Examples

or:

Note that the indices are counted starting from 0.

or: