Matrix Decompositions

What are some important matrix decompositions, and where are they used?

Answer

Some important matrix decompositions (from more restrictive to more general) are:

  • Cholesky decomposition: used for simulating multivariate normal random vectors.

  • Eigenvalue decomposition: used for PCA (via the covariance matrix).

  • QR decomposition: used for linear regression / least squares problems.

  • SVD (Singular Value Decomposition): can be used for PCA and for simulating multivariate normals, among other uses.

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