let a be the matrix of order 100, whose generic element is a_{ij}=\max(i,j) and let b=a^ta. the element of row 52 and column 64 of the choleski factor of b is approximately equal to: in matlab

To create matrix a with generic element a_{ij}=\max(i,j), you can use the following MATLAB code:

main.m
n = 100;       % order of the matrix
a = zeros(n);  % initialize the matrix with zeros

for i = 1:n
    for j = 1:n
        a(i, j) = max(i, j);
    end
end
157 chars
9 lines

To calculate the Cholesky factorization of b = a^T * a and find the element in row 52, column 64 of the Cholesky factor, you can use the following MATLAB code:

main.m
b = a' * a;  % calculate b = a^T * a

L = chol(b);  % calculate the Cholesky factor of b

element_5264 = L(52, 64);  % retrieve the element at row 52, column 64 of L
166 chars
6 lines

The value of the element at row 52, column 64 of the Cholesky factor of b can be found in the variable element_5264.