MATLAB: How to create a diagonal matrix with the semibandwidth of 4

diagonal matrix

how to create a matrix like this:

Best Answer

Hi Lin Hongbin
not sure if your picture contains some errors, A(3,1) looks suspicious to me...
look at this and tell me if it fits your wishes :)
a=1:10;
b=11:20;
c=21:30;
d=31:40;
n=length(a);
A=zeros(n);
% set the rest
for i=1:n % rows
        A(i,i:i+3)=[a(i),b(i),c(i),d(i)];
end
>> A
A =
     1    11    21    31     0     0     0     0     0     0     0     0     0
     0     2    12    22    32     0     0     0     0     0     0     0     0
     0     0     3    13    23    33     0     0     0     0     0     0     0
     0     0     0     4    14    24    34     0     0     0     0     0     0
     0     0     0     0     5    15    25    35     0     0     0     0     0
     0     0     0     0     0     6    16    26    36     0     0     0     0
     0     0     0     0     0     0     7    17    27    37     0     0     0
     0     0     0     0     0     0     0     8    18    28    38     0     0
     0     0     0     0     0     0     0     0     9    19    29    39     0
     0     0     0     0     0     0     0     0     0    10    20    30    40
if u cut off the first and last column it looks more like your picture (beside A(3,1) and A(3,4) etc is not d3 ...)
B=A(1:n,2:n+2)
B =
  11    21    31     0     0     0     0     0     0     0     0
   2    12    22    32     0     0     0     0     0     0     0
   0     3    13    23    33     0     0     0     0     0     0
   0     0     4    14    24    34     0     0     0     0     0
   0     0     0     5    15    25    35     0     0     0     0
   0     0     0     0     6    16    26    36     0     0     0
   0     0     0     0     0     7    17    27    37     0     0
   0     0     0     0     0     0     8    18    28    38     0
   0     0     0     0     0     0     0     9    19    29    39
   0     0     0     0     0     0     0     0    10    20    30
so either matrix A or B might be the answer.
But neither A nor B are quadratic. A has size n x n+3 and B: n x n+1
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