Generalize or restrict a few basic operators

base/operators.jl

@@ -525,8 +525,9 @@ julia> identity("Well, what did you expect?")
 """
 identity(x) = x
 
-+(x::Number) = x
-*(x::Number) = x
++(x) = x
+-(x) = (-1)*x
+*(x) = x
 (&)(x::Integer) = x
 (|)(x::Integer) = x
 xor(x::Integer) = x
@@ -626,7 +627,7 @@ julia> inv(A) * x
  -7.0
 ```
 """
-\(x,y) = adjoint(adjoint(y)/adjoint(x))
+\(x::Number, y::Number) = conj(conj(y)/conj(x))
 
 # Core <<, >>, and >>> take either Int or UInt as second arg. Signed shift
 # counts can shift in either direction, and are translated here to unsigned

stdlib/LinearAlgebra/src/adjtrans.jl

@@ -318,6 +318,8 @@ pinv(v::TransposeAbsVec, tol::Real = 0) = pinv(conj(v.parent)).parent
 
 ## left-division \
 \(u::AdjOrTransAbsVec, v::AdjOrTransAbsVec) = pinv(u) * v
+\(u::AdjointAbsVec, y::Number) = adjoint(conj(y) / u.parent)
+\(u::TransposeAbsVec, y::Number) = transpose(y / u.parent)
 
 
 ## right-division /

stdlib/LinearAlgebra/test/generic.jl

@@ -389,16 +389,13 @@ Base.:*(a::ModInt{n}, b::ModInt{n}) where {n} = ModInt{n}(a.k * b.k)
 Base.:-(a::ModInt{n}) where {n} = ModInt{n}(-a.k)
 Base.inv(a::ModInt{n}) where {n} = ModInt{n}(invmod(a.k, n))
 Base.:/(a::ModInt{n}, b::ModInt{n}) where {n} = a*inv(b)
+Base.:\(a::ModInt{n}, b::ModInt{n}) where {n} = inv(a)*b
 
 Base.zero(::Type{ModInt{n}}) where {n} = ModInt{n}(0)
 Base.zero(::ModInt{n}) where {n} = ModInt{n}(0)
 Base.one(::Type{ModInt{n}}) where {n} = ModInt{n}(1)
 Base.one(::ModInt{n}) where {n} = ModInt{n}(1)
 Base.conj(a::ModInt{n}) where {n} = a
-Base.adjoint(a::ModInt{n}) where {n} = ModInt{n}(conj(a))
-Base.transpose(a::ModInt{n}) where {n} = a # see Issue 20978
-LinearAlgebra.Adjoint(a::ModInt{n}) where {n} = adjoint(a)
-LinearAlgebra.Transpose(a::ModInt{n}) where {n} = transpose(a)
 
 @testset "Issue 22042" begin
  A = [ModInt{2}(1) ModInt{2}(0); ModInt{2}(1) ModInt{2}(1)]