orthogonal modal matrix m that transforms the covariance matrix c to the diagonal form. in javascript

To transform the covariance matrix c to diagonal matrix:

1. Compute the eigenvectors and eigenvalues of matrix c

2. Construct the matrix P from eigenvectors as columns

3. Transpose the matrix P to get the inverse transformation matrix P^-1

4. Obtain the diagonal matrix D from eigenvalues

5. The orthogonal matrix M is given by M = P^-1* D^(1/2)* P.

Here is the JavaScript code to obtain the orthogonal matrix M:

index.tsx
function transformToDiagonalMatrix(covarianceMatrix) {
    // Step 1: Compute the eigenvectors and eigenvalues of covariance matrix c
    const { eigenvectors, eigenvalues } = eig(covarianceMatrix);

    // Step 2: Construct the matrix P from eigenvectors as columns
    const P = eigenvectors;

    // Step 3: Transpose P to get the inverse transformation matrix P^-1
    const Pinv = numeric.inv(P);

    // Step 4: Obtain the diagonal matrix D from eigenvalues
    const D = numeric.diag(eigenvalues);

    // Step 5: Calculate orthogonal matrix M = P^-1 * D^(1/2) * P
    const Dsqrt = numeric.sqrt(D);
    const M = numeric.dot(numeric.dot(Pinv, Dsqrt), P);

    return M;
}
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Note: This code assumes that you have access to a library for computing eigenvectors and eigenvalues of a matrix (eig() function in this code). You can use any library of your choice that provides this functionality.

Also, this assumes that the numeric.js library is installed and numeric.dot() and numeric.inv() are available for matrix multiplication and matrix inversion, respectivley.