How to create a matrix where the value shifts to the write with each row? And how do I create a vector that increases and then decreases?

I need to make a square matrix that is 583x583. With every row, the values shift to the right and the values shift to the right are zeros. In other words, the matrix needs to be shaped like this:

F= [ F(1) 0 0......0

[ F(2) F(1) 0 0 .....0

[F(583) F(582)........F(1)]

The issue that I'm also having is creating the values for F. The values are based on a graph that increases and then decreases. So it has to be:

F=[10E-1 10 10E-1 10E-2 9E-3 8E-3 7E-3 6E-3........]. How do I create a for loop that will decrease the values like that?

Answer 1

[Matt J]

F=[10E-1 10 10E-1 10E-2 ,     (9:-1:1)*1e-3];

toeplitz(F,[F(1), zeros(1,numel(F)-1  )])

ans = 13×13

1.0000 0 0 0 0 0 0 0 0 0 0 0 0 10.0000 1.0000 0 0 0 0 0 0 0 0 0 0 0 1.0000 10.0000 1.0000 0 0 0 0 0 0 0 0 0 0 0.1000 1.0000 10.0000 1.0000 0 0 0 0 0 0 0 0 0 0.0090 0.1000 1.0000 10.0000 1.0000 0 0 0 0 0 0 0 0 0.0080 0.0090 0.1000 1.0000 10.0000 1.0000 0 0 0 0 0 0 0 0.0070 0.0080 0.0090 0.1000 1.0000 10.0000 1.0000 0 0 0 0 0 0 0.0060 0.0070 0.0080 0.0090 0.1000 1.0000 10.0000 1.0000 0 0 0 0 0 0.0050 0.0060 0.0070 0.0080 0.0090 0.1000 1.0000 10.0000 1.0000 0 0 0 0 0.0040 0.0050 0.0060 0.0070 0.0080 0.0090 0.1000 1.0000 10.0000 1.0000 0 0 0