Should the following example work?

```
julia> using LinearAlgebra
julia> using SparseArrays
julia> # 10x10 sparse matrix
A = sprand(10, 10, 1.0)
10×10 SparseMatrixCSC{Float64, Int64} with 100 stored entries:
0.904426 0.425966 0.678877 0.990534 … 0.00486748 0.625129 0.28918
0.908373 0.0387709 0.17868 0.725458 0.245102 0.0862697 0.632291
0.361639 0.387367 0.457368 0.369276 0.0896446 0.958725 0.170507
0.992062 0.344254 0.546643 0.780792 0.996618 0.427766 0.328221
0.877559 0.19974 0.123014 0.00153193 0.516185 0.372909 0.37089
0.396713 0.279064 0.855201 0.0253617 … 0.404998 0.934266 0.935675
0.656733 0.0671018 0.859334 0.427824 0.828616 0.920709 0.101263
0.682545 0.709925 0.173347 0.13505 0.351449 0.509649 0.263236
0.667382 0.247777 0.20485 0.37823 0.249513 0.711105 0.919538
0.185091 0.271876 0.971401 0.671663 0.956294 0.766601 0.786353
julia> # factorization with dense matrix
F = cholesky(Matrix(A'A))
Cholesky{Float64, Matrix{Float64}}
U factor:
10×10 UpperTriangular{Float64, Matrix{Float64}}:
2.24998 0.858844 1.30242 1.43303 … 1.32864 1.63633 1.30012
⋅ 0.689552 0.437529 0.0572014 0.132471 0.763297 0.261955
⋅ ⋅ 1.27031 0.51108 0.79303 0.99325 0.542768
⋅ ⋅ ⋅ 0.855286 -0.202569 -0.298744 -0.130929
⋅ ⋅ ⋅ ⋅ 0.0814408 0.101939 0.183558
⋅ ⋅ ⋅ ⋅ … -0.409493 0.350895 0.311987
⋅ ⋅ ⋅ ⋅ -0.0795898 0.0724291 0.901631
⋅ ⋅ ⋅ ⋅ 0.803321 -0.0278404 0.239681
⋅ ⋅ ⋅ ⋅ ⋅ 0.487393 -0.116216
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 0.301848
julia> # lower triangular is a valid AbstractMatrix
F.L * rand(10)
10-element Vector{Float64}:
0.6138698436089721
0.5057798279914256
0.7973250659194446
0.7477808021543471
0.49600451802224116
0.42332422693787697
0.7360032500412224
1.2133500519668785
1.2063489971211445
1.4239143574981488
julia> # factorization with sparse matrix
F = cholesky(A'A)
SuiteSparse.CHOLMOD.Factor{Float64}
type: LLt
method: simplicial
maxnnz: 55
nnz: 55
success: true
julia> # doesn't work, the L field doesn't implement getindex
F.L * rand(10)
ERROR: getindex not defined for SuiteSparse.CHOLMOD.FactorComponent{Float64, :L}
Stacktrace:
[1] error(::String, ::Type)
@ Base ./error.jl:42
[2] error_if_canonical_getindex(::IndexCartesian, ::SuiteSparse.CHOLMOD.FactorComponent{Float64, :L}, ::Int64, ::Int64)
@ Base ./abstractarray.jl:1231
[3] getindex
@ ./abstractarray.jl:1217 [inlined]
[4] _getindex
@ ./abstractarray.jl:1257 [inlined]
[5] getindex
@ ./abstractarray.jl:1218 [inlined]
[6] generic_matvecmul!(C::Vector{Float64}, tA::Char, A::SuiteSparse.CHOLMOD.FactorComponent{Float64, :L}, B::Vector{Float64}, _add::LinearAlgebra.MulAddMul{true, true, Bool, Bool})
@ LinearAlgebra ~/Desktop/julia-1.7.0/share/julia/stdlib/v1.7/LinearAlgebra/src/matmul.jl:759
[7] mul!
@ ~/Desktop/julia-1.7.0/share/julia/stdlib/v1.7/LinearAlgebra/src/matmul.jl:81 [inlined]
[8] mul!
@ ~/Desktop/julia-1.7.0/share/julia/stdlib/v1.7/LinearAlgebra/src/matmul.jl:275 [inlined]
[9] *(A::SuiteSparse.CHOLMOD.FactorComponent{Float64, :L}, x::Vector{Float64})
@ LinearAlgebra ~/Desktop/julia-1.7.0/share/julia/stdlib/v1.7/LinearAlgebra/src/matmul.jl:51
[10] top-level scope
@ REPL[41]:2
```

The cholesky documentation mentions a special case for sparse matrices, but I can’t find out how to extract the lower triangular or the `F.PtL`

as `AbstractMatrix`

for further processing.