## MatrixFactorizations.jl

A Julia package to contain non-standard matrix factorizations
Author JuliaLinearAlgebra
Popularity
16 Stars
Updated Last
1 Year Ago
Started In
March 2019

# MatrixFactorizations.jl

A Julia package to contain non-standard matrix factorizations. At the moment it implements the QL, RQ, and UL factorizations, a combined Cholesky factorization with inverse, and polar decompositions. In the future it may include other factorizations such as the LQ factorization.

## QL Factorization

The QL Factorization is analogous to the QR factorization but with a lower-triangular matrix:

```julia> using MatrixFactorizations

julia> A = randn(5,5);

julia> ql(A)
MatrixFactorizations.QL{Float64,Array{Float64,2}}
Q factor:
5×5 MatrixFactorizations.QLPackedQ{Float64,Array{Float64,2}}:
0.155574  -0.112555   -0.686362   -0.701064   0.0233276
0.363037  -0.0583277  -0.0329428   0.152682   0.916736
-0.670742   0.294355   -0.547867    0.347157   0.206843
-0.61094   -0.566041    0.324432   -0.353128   0.276396
0.144425  -0.759527   -0.349868    0.489877  -0.199681
L factor:
5×5 Array{Float64,2}:
-1.75734     0.0         0.0        0.0       0.0
-0.58336    -2.08515     0.0        0.0       0.0
0.0213518   0.0722477  -2.01325    0.0       0.0
0.930364   -0.46796    -0.322493  -2.9091    0.0
1.08725     0.746217    0.549688  -1.10194  -2.0581

julia> b = randn(5); ql(A) \ b ≈ A \ b
true```

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