Sum of elements of a matrix such that no row or column repeats

If i choose an element of a matrix than the next element used should be from different row and different column. If there is a nxn matrix then the sum of n elements of the matrix should come from the elements of different row and different column.

Answer 1

[Torsten]

p = randperm(n);

sum = 0.0;

for k = 1:n

sum = sum + a(k,p(k));

end

where a is the nxn matrix.

[Lovish Goyal]

How do we know that any column is not repeated here

[Torsten]

Because in p, no number is repeated.

[Lovish Goyal]

Is there any way that we can also reject all the main diaginal elements. like k should not be equal to p(k).

[Torsten]

p = randperm(n) ;

while any(p==(1:n))

p = randperm(n);

end

% Rest is the same