Basically, if for every row, the absolute value of the entry along the main diagonal is larger than the sum of the absolute values of all other entries on that row. Write a function whose input is a matrix and will determine (true/false) if a matrix is diagonally dominant. Show that your function works as expected.

Check the explanation

Explanation:

MATLAB code:

%----------------------

function result = dominant(A)

% matrix dimensions

d = size(A);

% for loop over rows

for i = 1:d

% sum of row elements except diagonal element

sum_row =0;

% for loop over columns

for j = 1:d

% adding each elements to sum variable

sum_row = sum_row+ abs(A(i,j));

end

%subratcting diagonal element

sum_row = sum_row-abs(A(i,i));

%checking dominant condition

% failed once means matrix is not diagonal dominant

if abs(A(i,i))< sum_row

result = 'false';

return;

end

end

% dominant condition not failed

result = 'true';

end

% matrix A

A = [ 3 -2 1; 1 -3 2; 1 2 6]

% result

result = dominant(A)

% matrix A

A = [ -2 1 2; 1 3 2; 1 -2 0]

% result

result = dominant(A)

%----------------------

Kindly check the attached output image below.