how can I write this in a compact form? can anyone suggest a single line code for it

yita_mn = [

0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1;

1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1;

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0

];

Answer 1

[John D'Errico]

At its heart, this is just a basic circulant matrix. So use a tool that will do that. I posted such a tool on the file exchange. But you can just use gallery.

n = 8; % an 8x8 circulant matrix of that form
M = gallery('circul',[0 1,zeros(1,n-3),1])

M = 8×8

0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0

Or you can view this as a Toeplitz matrix. Toeplitz matrices are a close second cousin to circulant matrices. Your matrix is always symmetric, so a symmetric Toeplitz matrix can be formed by just supplying the first row or column.

M2 = toeplitz([0 1,zeros(1,n-3),1])

M2 = 8×8

0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0

Of course there are other ways to do it. Since your matrix is actually quite sparse, you could build it as a sparse banded matrix. The virtue of that is if n is large, (as it often will be in applications like this) then you use efficient sparse storage, as well as efficient computations thereafter with that matrix.

I'll use n=50 here, but typically n might be a number in the thousands or more, if you are really needing to use a sparse matrix. 50 is large enough that you can visualize the banded structure easily, yet not too large that you cannot see the dots. (If I made n=10000, then you might not even see the dots in the corners, or see the line down the middle as actually a pair of bands just above and below the main diagonal.)

n = 50;
M3 = spdiags(ones(n,4),[-n+1, -1, 1, n-1],n,n);
spy(M3)

whos M3

  Name       Size            Bytes  Class     Attributes

  M3        50x50             2008  double    sparse    

As you can see, M3 is a sparse version of the matrix you want to build.

Answer 2

[Bruno Luong]

n = 8;
ismember(mod((1:n)-(1:n)',n),[1 n-1])

ans = 8×8 logical array
   0   1   0   0   0   0   0   1
   1   0   1   0   0   0   0   0
   0   1   0   1   0   0   0   0
   0   0   1   0   1   0   0   0
   0   0   0   1   0   1   0   0
   0   0   0   0   1   0   1   0
   0   0   0   0   0   1   0   1
   1   0   0   0   0   0   1   0

Answer 3

[Sargondjani]

You can do something like:

A=[zeros(1,10);eye(9),zeros(9,1)]+ ....    

Try to figure out the details yourself...

Answer 4

[Walter Roberson]

https://www.mathworks.com/help/matlab/ref/toeplitz.html#buxdtu9

circulant matrix

Or you could add two diagonal matrices

[Walter Roberson]

n = 8;
circshift(diag(ones(1,n)),1) + circshift(diag(ones(1,n)),-1)

ans = 8×8

0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0