how to create this matrix?

can anyone help me to construct this matrix

blj=(-2)^j-l if l<j
blj=1        if l=j
blj=0        if l>j

Answer 1

[Brian Hart]

Hi diadalina,

I think it would look something like this...

iLength = 5; %rows
jLength = 7; %cols

b=zeros(iLength, jLength);

for i = 1:iLength
    for j = 1:jLength
        if i == j; b(i,j) = 1; end
        if i < j; b(i,j) = (-2)^(j-i); end
    end
end

disp(b)
            

gives a result of:

     1    -2     4    -8    16   -32    64
     0     1    -2     4    -8    16   -32
     0     0     1    -2     4    -8    16
     0     0     0     1    -2     4    -8
     0     0     0     0     1    -2     4

[Guillaume]

It is unclear if the formula in the question is as written or which would make more sense. One thing for sure, it's not likely to be which is what you calculate.

[Brian Hart]

Yep, missed a set of parenthesis. Corrected, thanks.

Answer 2

[Guillaume]

Assume your formula is and not what you have written:

nrows = 5;   %number of rows. You haven't specified
ncols = 7;   %number of columns. You haven't specified

b = toeplitz([1, zeros(1, nrows-1)], (-2).^(0:ncols-1))

If the formula is what you have actually written, , then

b = triu((-2).^(1:ncols) - (1:nrows)', 1) + eye(nrows, ncols)

[Stephan]

+1

Answer 3

[Stephan]

Hi,

do you want a square matrix? Is the calculation correct without any brackets? My calculation follows the way you wrote the formula - if wrong set the brackets corresponding to your expected result.

Then try:

k=3;
[m,n]=meshgrid(1:k);
A=triu((-2).^n-m,1) + eye(k)

Best regards

Stephan