Eigenvalue and factor models: how to get the orthogonal matrix?

Hi everyone, I would like to know if there is a command to form factor models and get the orthogonal matrix in matlab. For instance, let QAQ = covariance matrix of x and A is a diagonal matrix of eigenvalues of the matrix cov(x) and Q is an orthogonal matrix whose columns are standardized eigenvectors. How can I get the Q...the orthogonal matrix in matlab?

Thank you,

Answer 1

[Prateekshya]

Hello Charles,

You can use the eig function to get the orthogonal matrix in MATLAB. Here is a sample code for the same:

% Sample data matrix x (e.g., each row is an observation, each column is a variable)
x = randn(100, 5); % Example: 100 observations of 5 variables

% Compute the covariance matrix of x
covMatrix = cov(x);

% Use the eig function to get eigenvectors and eigenvalues
[Q, A] = eig(covMatrix);

% Q is the orthogonal matrix of standardized eigenvectors
% A is the diagonal matrix of eigenvalues

% Display the orthogonal matrix Q
disp('Orthogonal matrix Q:');
disp(Q);

% Display the diagonal matrix A of eigenvalues
disp('Diagonal matrix of eigenvalues A:');
disp(diag(A));

You can modify the code according to your requirement.

I hope this helps!