matrix-decompositions.py

https://github.com/marimo-team/gallery-examples/blob/main/notebooks/math/matrix-decompositions.py

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SVD: A=UΣV⊤A = U \Sigma V^\top


UU and VV are orthogonal matrices, Σ\Sigma is diagonal with singular values. Reveals the rank, range, and null space of a matrix.
||(=||)
||(\times||)
||(\times||)
QR: A=QRA = QR


QQ is orthogonal, RR is upper triangular. Used for solving least squares problems and computing eigenvalues.
||(=||)
||(\times||)
LU: A=PLUA = PLU


PP is a permutation matrix, LL is lower triangular, UU is upper triangular. Efficient for solving linear systems via forward/backward substitution.
||(=||)
||(\times||)
||(\times||)