MatrixFactorization is the virtual class of
factorizations of \(m \times n\) matrices \(A\),
having the general form
$$P_{1} A P_{2} = A_{1} \cdots A_{p}$$
or (equivalently)
$$A = P_{1}' A_{1} \cdots A_{p} P_{2}'$$
where \(P_{1}\) and \(P_{2}\) are permutation matrices.
Factorizations requiring symmetric \(A\) have the constraint
\(P_{2} = P_{1}'\), and factorizations without row
or column pivoting have the constraints
\(P_{1} = I_{m}\) and \(P_{2} = I_{n}\),
where \(I_{m}\) and \(I_{n}\) are the
\(m \times m\) and \(n \times n\) identity matrices.
CholeskyFactorization, BunchKaufmanFactorization,
SchurFactorization, LU, and QR are the virtual
subclasses of MatrixFactorization containing all Cholesky,
Bunch-Kaufman, Schur, LU, and QR factorizations, respectively.
Classes extending CholeskyFactorization, namely
Cholesky, pCholesky,
and CHMfactor.
Classes extending BunchKaufmanFactorization, namely
BunchKaufman and pBunchKaufman.
Classes extending SchurFactorization, namely
Schur.
Classes extending LU, namely
denseLU and sparseLU.
Classes extending QR, namely sparseQR.
Generic functions Cholesky, BunchKaufman,
Schur, lu, and qr for
computing factorizations.
Generic functions expand1 and expand2
for constructing matrix factors from MatrixFactorization
objects.
showClass("MatrixFactorization")
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