LinearAlgebra excision from sysimg.

I was thinking about JuliaLang/julia#51432 this morning and I was curious how bad it would be for LinearAlgebra.

Using:
```
import LinearAlgebra

function allinbase(T)
T = Base.unwrap_unionall(T)
if T isa Union
return allinbase(T.a) && allinbase(T.b)
end
return T.name.module == Base || T.name.module == Core
end

for name in names(Base)
obj = getglobal(Base, name)
if obj isa Function
candidates = methods(obj, LinearAlgebra)
for candidate in candidates
sig = Base.tuple_type_tail(candidate.sig)
allInBase = true
while sig !== Tuple{}
T = Base.tuple_type_head(sig)
sig = Base.tuple_type_tail(sig)
allInBase &= allinbase(T)
allInBase || break
end
if allInBase
println(candidate)
end
end
end
end
```

In 1.10-beta.2 we have the following candidates:

```
adjoint(B::Union{BitMatrix, BitVector}) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/bitarray.jl:237
adjoint(a::AbstractArray) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/transpose.jl:3
*(A::AbstractMatrix, B::AbstractMatrix, C::AbstractMatrix, D::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/matmul.jl:1229
*(A::AbstractMatrix, B::AbstractMatrix, C::AbstractMatrix, x::AbstractVector) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/matmul.jl:1221
*(A::AbstractMatrix, B::AbstractMatrix, x::AbstractVector) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/matmul.jl:1144
*(A::AbstractMatrix, B::AbstractMatrix, C::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/matmul.jl:1160
*(a::AbstractVector, B::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/matmul.jl:63
*(A::AbstractMatrix{T}, x::AbstractVector{S}) where {T, S} @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/matmul.jl:55
*(A::AbstractMatrix, B::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/matmul.jl:104
\(a::AbstractVector, b::AbstractArray) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/generic.jl:1129
^(::Irrational{:ℯ}, A::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:645
acos(A::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1135
acosh(A::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1215
acot(A::AbstractMatrix{T}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1289
acoth(A::AbstractMatrix{T}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1292
acsc(A::AbstractMatrix{T}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1289
acsch(A::AbstractMatrix{T}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1292
adjoint(B::Union{BitMatrix, BitVector}) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/bitarray.jl:237
adjoint(a::AbstractArray) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/transpose.jl:3
asec(A::AbstractMatrix{T}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1289
asech(A::AbstractMatrix{T}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1292
asin(A::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1166
asinh(A::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1234
atan(A::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1197
atanh(A::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1252
cis(A::AbstractMatrix{<:Union{Float32, Float64, Int16, Int32, Int64, Int8, UInt16, UInt32, UInt64, UInt8, Complex{<:Union{Float32, Float64, Int16, Int32, Int64, Int8, UInt16, UInt32, UInt64, UInt8}}, Rational{<:Union{Float32, Float64, Int16, Int32, Int64, Int8, UInt16, UInt32, UInt64, UInt8}}}}) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:616
cis(A::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:615
convert(::Type{T}, A::AbstractMatrix) where T<:Diagonal @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/diagonal.jl:100
convert(::Type{T}, m::AbstractMatrix) where T<:Bidiagonal @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/bidiag.jl:220
copyto!(dest::Array{T}, rdest::AbstractRange{Ti}, src::Array{T}, rsrc::AbstractRange{Ti}) where {T<:Union{Float32, Float64, ComplexF64, ComplexF32}, Ti<:Integer} @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/blas.jl:2121
cos(A::AbstractMatrix{<:Complex}) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:946
cos(A::AbstractMatrix{<:Real}) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:939
cosh(A::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1072
cot(A::AbstractMatrix{T}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1272
coth(A::AbstractMatrix{T}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1277
csc(A::AbstractMatrix{T}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1272
csch(A::AbstractMatrix{T}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1277
eltype(::Type{<:LinearAlgebra.AbstractQ{T}}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/abstractq.jl:10
eltype(::Type{<:LinearAlgebra.Factorization{T}}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/factorization.jl:40
eltype(::Type{LinearAlgebra.UniformScaling{T}}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/uniformscaling.jl:86
exp(A::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:594
inv(A::AbstractMatrix{T}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/generic.jl:1048
isapprox(x::AbstractArray, y::AbstractArray; atol, rtol, nans, norm) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/generic.jl:1785
isone(A::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:16
kron(a::BitMatrix, b::BitMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/bitarray.jl:131
kron(a::BitVector, b::BitVector) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/bitarray.jl:107
kron(a::AbstractVector{T}, b::AbstractVector{S}) where {T, S} @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:469
kron!(R::BitMatrix, a::BitMatrix, b::BitMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/bitarray.jl:114
kron!(R::BitVector, a::BitVector, b::BitVector) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/bitarray.jl:95
kron!(c::AbstractVector, a::AbstractVector, b::AbstractVector) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:370
log(A::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:798
one(::Type{LinearAlgebra.UniformScaling{T}}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/uniformscaling.jl:130
oneunit(::Type{LinearAlgebra.UniformScaling{T}}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/uniformscaling.jl:132
promote_rule(::Type{Matrix{T}}, ::Type{<:LinearAlgebra.Bidiagonal{S, V} where V<:AbstractVector{S}}) where {T, S} @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/bidiag.jl:202
promote_rule(::Type{<:AbstractMatrix{T}}, ::Type{<:LinearAlgebra.AbstractQ{T}}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/abstractq.jl:21
promote_rule(A::Type{<:LinearAlgebra.Diagonal{<:Any, V}}, B::Type{<:LinearAlgebra.Diagonal{<:Any, W}}) where {V, W} @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/diagonal.jl:17
promote_rule(::Type{<:LinearAlgebra.Tridiagonal}, ::Type{<:LinearAlgebra.Bidiagonal}) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/bidiag.jl:215
promote_rule(::Type{<:LinearAlgebra.Tridiagonal{T, V} where V<:AbstractVector{T}}, ::Type{<:LinearAlgebra.Bidiagonal{S, V} where V<:AbstractVector{S}}) where {T, S} @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/bidiag.jl:213
sec(A::AbstractMatrix{T}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1272
sech(A::AbstractMatrix{T}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1277
sin(A::AbstractMatrix{<:Complex}) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:979
sin(A::AbstractMatrix{<:Real}) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:972
sincos(A::AbstractMatrix{<:Real}) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1013
sincos(A::AbstractMatrix{<:Complex}) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1024
sinh(A::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1086
sqrt(A::AbstractMatrix{T}) where T<:Union{Real, Complex} @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:877
tan(A::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1058
tanh(A::AbstractMatrix) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:1100
transpose(B::Union{BitMatrix, BitVector}) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/bitarray.jl:238
transpose(a::AbstractArray) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/transpose.jl:4
zero(::Type{LinearAlgebra.UniformScaling{T}}) where T @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/uniformscaling.jl:134
sqrt(A::AbstractMatrix{T}) where T<:Union{Real, Complex} @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:877
isapprox(x::AbstractArray, y::AbstractArray; atol, rtol, nans, norm) @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-beta2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/generic.jl:1785
```

This is surprisingly managable and even include's some false-positives. E.g. `promote_rule`/`convert`.

Start by reading JuliaLang/julia#51432 and inspecting the listed LinearAlgebra methods in dense.jl, generic.jl, matmul.jl, bitarray.jl, diagonal.jl, bidiag.jl, abstractq.jl, factorization.jl, uniformscaling.jl, and transpose.jl. Done means the identified LinearAlgebra functionality is no longer included in the sysimg while its intended behavior remains available.

Written by the indexing model from the issue text.