Include HermOrSym in character-based mul! dispatch

stdlib/LinearAlgebra/src/LinearAlgebra.jl

@@ -457,6 +457,34 @@ const ⋅ = dot
 const × = cross
 export ⋅, ×
 
+wrapper_char(::AbstractArray) = 'N'
+wrapper_char(::Adjoint) = 'C'
+wrapper_char(::Adjoint{<:Real}) = 'T'
+wrapper_char(::Transpose) = 'T'
+wrapper_char(A::Hermitian) = A.uplo == 'U' ? 'H' : 'h'
+wrapper_char(A::Hermitian{<:Real}) = A.uplo == 'U' ? 'S' : 's'
+wrapper_char(A::Symmetric) = A.uplo == 'U' ? 'S' : 's'
+
+function wrap(A::AbstractVecOrMat, tA::AbstractChar)
+    if tA == 'N'
+        return A
+    elseif tA == 'T'
+        return transpose(A)
+    elseif tA == 'C'
+        return adjoint(A)
+    elseif tA == 'H'
+        return Hermitian(A, :U)
+    elseif tA == 'h'
+        return Hermitian(A, :L)
+    elseif tA == 'S'
+        return Symmetric(A, :U)
+    else # tA == 's'
+        return Symmetric(A, :L)
+    end
+end
+
+_unwrap(A::AbstractVecOrMat) = A
+
 ## convenience methods
 ## return only the solution of a least squares problem while avoiding promoting
 ## vectors to matrices.

stdlib/LinearAlgebra/src/adjtrans.jl

@@ -94,11 +94,8 @@ inplace_adj_or_trans(::Type{<:AbstractArray}) = copyto!
 inplace_adj_or_trans(::Type{<:Adjoint}) = adjoint!
 inplace_adj_or_trans(::Type{<:Transpose}) = transpose!
 
-adj_or_trans_char(::T) where {T<:AbstractArray} = adj_or_trans_char(T)
-adj_or_trans_char(::Type{<:AbstractArray}) = 'N'
-adj_or_trans_char(::Type{<:Adjoint}) = 'C'
-adj_or_trans_char(::Type{<:Adjoint{<:Real}}) = 'T'
-adj_or_trans_char(::Type{<:Transpose}) = 'T'
+_unwrap(A::Adjoint)   = parent(A)
+_unwrap(A::Transpose) = parent(A)
 
 Base.dataids(A::Union{Adjoint, Transpose}) = Base.dataids(A.parent)
 Base.unaliascopy(A::Union{Adjoint,Transpose}) = typeof(A)(Base.unaliascopy(A.parent))