Lesson 5: Matrix building functions

Convenient matrix building functions are

eye identity matrix
zeros matrix of zeros
ones matrix of ones
diag see below
triu upper triangular part of a matrix
tril lower triangular part of a matrix
rand randomly generated matrix
hilb Hilbert matrix
magic magic square

For example, zeros(m,n) produces an m × n matrix of zeros and zeros(n) produces an n × n one; if A is a matrix, then zeros(A) produces a matrix of zeros of the same size as A.

If x is a vector, diag(x) is the diagonal matrix with x down the diagonal; if A is a square matrix:

     A =
         1 2 3
         4 5 6
         7 8 9
then diag(A) is a vector consisting of the diagonal of A. What is diag(diag(A))? Try it.

Matrices can be built from blocks. For example, if A is a 3-by-3 matrix, then

	B = [A, zeros(3,2); ones(2,3), eye(2)]
will build a certain 5-by-5 matrix. Try it!