How can I create a triangular matrix based on a vector, in MATLAB?

Question

Let's say I've got a vector like this one:

A = [101:105]

Which is really:

[ 101, 102, 103, 104, 105 ]

And I'd like to use only vector/matrix functions and operators to produces the matrix:

101 102 103 104 105
102 103 104 105 0
103 104 105 0   0
104 105 0   0   0
105 0   0   0   0

or the following matrix:

101 102 103 104 105
0   101 102 103 104
0   0   101 102 103
0   0   0   101 102
0   0   0   0   101

Any ideas anyone?

(I'm very much a novice in MATLAB, but I've been saddled this stuff...)

Answer 1

The way I'd go about it is to create a matrix A:

101 102 103 104 105
101 102 103 104 105
101 102 103 104 105
101 102 103 104 105
101 102 103 104 105

And then find a matrix B such that when you multiply A*B you'll get the result you want. Basically do the linear algebra on paper first and then have Matlab do the calculation.

Answer 2

hankel(A) will get you the first matrix

triu(toeplitz(A)) will get you the second one.

--Loren

Answer 3

The best solutions are listed by Loren. It's also possible to create these matrices using SPDIAGS:

vec = 101:105;
A = full(spdiags(repmat(vec,5,1),0:4,5,5));  % The second matrix
B = fliplr(full(spdiags(repmat(fliplr(vec),5,1),0:4,5,5)));  % The first matrix

I recall creating banded matrices like this before I found out about some of the built-in functions Loren mentioned. It's not nearly as simple and clean as using those, but it worked. =)