how can i compute Aij?

this is the question i have. my instructor is not really helpful with this and i need help.

[the cyclist]

What you have posted is not a question; it is a homework problem.

People here will help, but they will not do your homework for you.

What have you tried? What is the "existing code"? (Please post it.) Where is your code? (Please post it.) Where are you stuck? What is it that you do not understand?

[Gurpreet]

this is the code i have so far: as per my instructor:

% Function to generate n x n matrix with pseudo-random entries between 0 and 1
generateMatrix = @(n) rand(n);
% Parameters
delta_n = 200;
k_values = 1:10;
% Initialize arrays to store condition numbers
condition_numbers_A = zeros(size(k_values));
condition_numbers_B = zeros(size(k_values));
condition_numbers_C = zeros(size(k_values));
condition_numbers_D = zeros(size(k_values));
% Loop over k values
for k = k_values
    n = k * delta_n;
    
    % Generate matrix A
    A = generateMatrix(n);
    
    % Generate matrices B, C, D based on the rules
    B = A;
    C = A;
    D = A;
    
    % Modify elements based on rules
    for i = 1:n
        B(i, i) = 10;
        C(i, i) = 20;
        D(i, i) = 100;
    end
    
    % Calculate condition numbers
    condition_numbers_A(k) = cond(A);
    condition_numbers_B(k) = cond(B);
    condition_numbers_C(k) = cond(C);
    condition_numbers_D(k) = cond(D);
end
% Plot results using semilogy
figure;
semilogy(k_values * delta_n, condition_numbers_A, 'b', 'LineWidth', 2, 'DisplayName', 'A');
hold on;
semilogy(k_values * delta_n, condition_numbers_B, 'g', 'LineWidth', 2, 'DisplayName', 'B');
semilogy(k_values * delta_n, condition_numbers_C, 'r', 'LineWidth', 2, 'DisplayName', 'C');
semilogy(k_values * delta_n, condition_numbers_D, 'm', 'LineWidth', 2, 'DisplayName', 'D');
xlabel('Matrix Size (nk)');
ylabel('Condition Number (log scale)');
title('Condition Numbers of Matrices A, B, C, D');
legend('Location', 'Best');
grid on;
hold off;

it doesnt run however, and i am really confused

[Torsten]

Works for me (at least up to k=10) (see above).

[Gurpreet]

this is what im getting:

In untitled2 (line 32)

condition_numbers_A(k) = cond(A);

In untitled2 (line 33)

condition_numbers_B(k) = cond(B);

i ran it four times and then came to answers :(

Answer 1

[Les Beckham]

It appears to work. I ran it for only 2 values of k as it was timing out here in Answers when running with 20 values of k.

What do you mean "it doesn't run"? What are you seeing? Are you getting an error message? If so, cut and paste it here (all of the red or orange text in the command window.

% Function to generate n x n matrix with pseudo-random entries between 0 and 1
generateMatrix = @(n) rand(n);
% Parameters
delta_n = 200;
k_values = 1:2; % was 1:20
% Initialize arrays to store condition numbers
condition_numbers_A = zeros(size(k_values));
condition_numbers_B = zeros(size(k_values));
condition_numbers_C = zeros(size(k_values));
condition_numbers_D = zeros(size(k_values));
% Loop over k values
for k = k_values
    n = k * delta_n;
    
    % Generate matrix A
    A = generateMatrix(n);
    
    % Generate matrices B, C, D based on the rules
    B = A;
    C = A;
    D = A;
    
    % Modify elements based on rules
    for i = 1:n
        B(i, i) = 10;
        C(i, i) = 20;
        D(i, i) = 100;
    end
    
    % Calculate condition numbers
    condition_numbers_A(k) = cond(A);
    condition_numbers_B(k) = cond(B);
    condition_numbers_C(k) = cond(C);
    condition_numbers_D(k) = cond(D);
end
% Plot results using semilogy
figure;
semilogy(k_values * delta_n, condition_numbers_A, 'b', 'LineWidth', 2, 'DisplayName', 'A');
hold on;
semilogy(k_values * delta_n, condition_numbers_B, 'g', 'LineWidth', 2, 'DisplayName', 'B');
semilogy(k_values * delta_n, condition_numbers_C, 'r', 'LineWidth', 2, 'DisplayName', 'C');
semilogy(k_values * delta_n, condition_numbers_D, 'm', 'LineWidth', 2, 'DisplayName', 'D');
xlabel('Matrix Size (nk)');
ylabel('Condition Number (log scale)');
title('Condition Numbers of Matrices A, B, C, D');
legend('Location', 'Best');
grid on;
hold off;

[Gurpreet]

i tried on a different computer and it ran!!!

thank you all for your help :)

[Les Beckham]

You are quite welcome.