2. Matrix factorizations#

  • Singular Value Decomposition (SVD)

  • Spectral decomposition Eigenvalues, eigenvectors; Jordan canonical formula…

  • QR

  • LU

  • Schur

  • Cholesky Symmetric positive definite matrices have Choleski decomposition,

    \[\mathbf{M} = \mathbf{L} \mathbf{L}^* \ ,\]

    with \(\mathbf{L}\) lower triangular matrix. And thus quite easy to “invert”, for solving linear systems.