diff --git a/stdlib/LinearAlgebra/src/LinearAlgebra.jl b/stdlib/LinearAlgebra/src/LinearAlgebra.jl
index a42ca934e17a61..dad5e5c81cdda7 100644
--- a/stdlib/LinearAlgebra/src/LinearAlgebra.jl
+++ b/stdlib/LinearAlgebra/src/LinearAlgebra.jl
@@ -516,32 +516,56 @@ const ⋅ = dot
 const × = cross
 export ⋅, ×
 
+# Separate the char corresponding to the wrapper from that corresponding to the uplo
+# In most cases, the former may be constant-propagated, while the latter usually can't be.
+# This improves type-inference in wrap for Symmetric/Hermitian matrices
+# A WrapperChar is equivalent to `isuppertri ? uppercase(wrapperchar) : lowercase(wrapperchar)`
+struct WrapperChar <: AbstractChar
+    wrapperchar :: Char
+    isuppertri :: Bool
+end
+function Base.Char(w::WrapperChar)
+    T = w.wrapperchar
+    if T ∈ ('N', 'T', 'C') # known cases where isuppertri is true
+        T
+    else
+        _isuppertri(w) ? uppercase(T) : lowercase(T)
+    end
+end
+Base.codepoint(w::WrapperChar) = codepoint(Char(w))
+WrapperChar(n::UInt32) = WrapperChar(Char(n))
+WrapperChar(c::Char) = WrapperChar(c, isuppercase(c))
+# We extract the wrapperchar so that the result may be constant-propagated
+# This doesn't return a value of the same type on purpose
+Base.uppercase(w::WrapperChar) = uppercase(w.wrapperchar)
+Base.lowercase(w::WrapperChar) = lowercase(w.wrapperchar)
+_isuppertri(w::WrapperChar) = w.isuppertri
+_isuppertri(x::AbstractChar) = isuppercase(x) # compatibility with earlier Char-based implementation
+_uplosym(x) = _isuppertri(x) ? (:U) : (:L)
+
 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'
+wrapper_char(A::Hermitian) =  WrapperChar('H', A.uplo == 'U')
+wrapper_char(A::Hermitian{<:Real}) = WrapperChar('S', A.uplo == 'U')
+wrapper_char(A::Symmetric) = WrapperChar('S', A.uplo == 'U')
 
 Base.@constprop :aggressive function wrap(A::AbstractVecOrMat, tA::AbstractChar)
     # merge the result of this before return, so that we can type-assert the return such
     # that even if the tmerge is inaccurate, inference can still identify that the
     # `_generic_matmatmul` signature still matches and doesn't require missing backedges
-    B = if tA == 'N'
+    tA_uc = uppercase(tA)
+    B = if tA_uc == 'N'
         A
-    elseif tA == 'T'
+    elseif tA_uc == 'T'
         transpose(A)
-    elseif tA == 'C'
+    elseif tA_uc == 'C'
         adjoint(A)
-    elseif tA == 'H'
-        Hermitian(A, :U)
-    elseif tA == 'h'
-        Hermitian(A, :L)
-    elseif tA == 'S'
-        Symmetric(A, :U)
-    else # tA == 's'
-        Symmetric(A, :L)
+    elseif tA_uc == 'H'
+        Hermitian(A, _uplosym(tA))
+    elseif tA_uc == 'S'
+        Symmetric(A, _uplosym(tA))
     end
     return B::AbstractVecOrMat
 end
diff --git a/stdlib/LinearAlgebra/src/matmul.jl b/stdlib/LinearAlgebra/src/matmul.jl
index 9ed8bd1b677aa0..9c74addd6b69c2 100644
--- a/stdlib/LinearAlgebra/src/matmul.jl
+++ b/stdlib/LinearAlgebra/src/matmul.jl
@@ -364,14 +364,18 @@ lmul!(A, B)
 # aggressive constant propagation makes mul!(C, A, B) invoke gemm_wrapper! directly
 Base.@constprop :aggressive function generic_matmatmul!(C::StridedMatrix{T}, tA, tB, A::StridedVecOrMat{T}, B::StridedVecOrMat{T},
                                     _add::MulAddMul=MulAddMul()) where {T<:BlasFloat}
-    if all(in(('N', 'T', 'C')), (tA, tB))
-        if tA == 'T' && tB == 'N' && A === B
+    # We convert the chars to uppercase to potentially unwrap a WrapperChar,
+    # and extract the char corresponding to the wrapper type
+    tA_uc, tB_uc = uppercase(tA), uppercase(tB)
+    # the map in all ensures constprop by acting on tA and tB individually, instead of looping over them.
+    if all(map(in(('N', 'T', 'C')), (tA_uc, tB_uc)))
+        if tA_uc == 'T' && tB_uc == 'N' && A === B
             return syrk_wrapper!(C, 'T', A, _add)
-        elseif tA == 'N' && tB == 'T' && A === B
+        elseif tA_uc == 'N' && tB_uc == 'T' && A === B
             return syrk_wrapper!(C, 'N', A, _add)
-        elseif tA == 'C' && tB == 'N' && A === B
+        elseif tA_uc == 'C' && tB_uc == 'N' && A === B
             return herk_wrapper!(C, 'C', A, _add)
-        elseif tA == 'N' && tB == 'C' && A === B
+        elseif tA_uc == 'N' && tB_uc == 'C' && A === B
             return herk_wrapper!(C, 'N', A, _add)
         else
             return gemm_wrapper!(C, tA, tB, A, B, _add)
@@ -379,13 +383,13 @@ Base.@constprop :aggressive function generic_matmatmul!(C::StridedMatrix{T}, tA,
     end
     alpha, beta = promote(_add.alpha, _add.beta, zero(T))
     if alpha isa Union{Bool,T} && beta isa Union{Bool,T}
-        if (tA == 'S' || tA == 's') && tB == 'N'
+        if tA_uc == 'S' && tB_uc == 'N'
             return BLAS.symm!('L', tA == 'S' ? 'U' : 'L', alpha, A, B, beta, C)
-        elseif (tB == 'S' || tB == 's') && tA == 'N'
+        elseif tA_uc == 'N' && tB_uc == 'S'
             return BLAS.symm!('R', tB == 'S' ? 'U' : 'L', alpha, B, A, beta, C)
-        elseif (tA == 'H' || tA == 'h') && tB == 'N'
+        elseif tA_uc == 'H' && tB_uc == 'N'
             return BLAS.hemm!('L', tA == 'H' ? 'U' : 'L', alpha, A, B, beta, C)
-        elseif (tB == 'H' || tB == 'h') && tA == 'N'
+        elseif tA_uc == 'N' && tB_uc == 'H'
             return BLAS.hemm!('R', tB == 'H' ? 'U' : 'L', alpha, B, A, beta, C)
         end
     end
@@ -395,7 +399,11 @@ end
 # Complex matrix times (transposed) real matrix. Reinterpret the first matrix to real for efficiency.
 Base.@constprop :aggressive function generic_matmatmul!(C::StridedVecOrMat{Complex{T}}, tA, tB, A::StridedVecOrMat{Complex{T}}, B::StridedVecOrMat{T},
                     _add::MulAddMul=MulAddMul()) where {T<:BlasReal}
-    if all(in(('N', 'T', 'C')), (tA, tB))
+    # We convert the chars to uppercase to potentially unwrap a WrapperChar,
+    # and extract the char corresponding to the wrapper type
+    tA_uc, tB_uc = uppercase(tA), uppercase(tB)
+    # the map in all ensures constprop by acting on tA and tB individually, instead of looping over them.
+    if all(map(in(('N', 'T', 'C')), (tA_uc, tB_uc)))
         gemm_wrapper!(C, tA, tB, A, B, _add)
     else
         _generic_matmatmul!(C, wrap(A, tA), wrap(B, tB), _add)
@@ -434,18 +442,19 @@ Base.@constprop :aggressive function gemv!(y::StridedVector{T}, tA::AbstractChar
     mA == 0 && return y
     nA == 0 && return _rmul_or_fill!(y, β)
     alpha, beta = promote(α, β, zero(T))
+    tA_uc = uppercase(tA) # potentially convert a WrapperChar to a Char
     if alpha isa Union{Bool,T} && beta isa Union{Bool,T} &&
         stride(A, 1) == 1 && abs(stride(A, 2)) >= size(A, 1) &&
         !iszero(stride(x, 1)) && # We only check input's stride here.
-        if tA in ('N', 'T', 'C')
+        if tA_uc in ('N', 'T', 'C')
             return BLAS.gemv!(tA, alpha, A, x, beta, y)
-        elseif tA in ('S', 's')
+        elseif tA_uc == 'S'
             return BLAS.symv!(tA == 'S' ? 'U' : 'L', alpha, A, x, beta, y)
-        elseif tA in ('H', 'h')
+        elseif tA_uc == 'H'
             return BLAS.hemv!(tA == 'H' ? 'U' : 'L', alpha, A, x, beta, y)
         end
     end
-    if tA in ('S', 's', 'H', 'h')
+    if tA_uc in ('S', 'H')
         # re-wrap again and use plain ('N') matvec mul algorithm,
         # because _generic_matvecmul! can't handle the HermOrSym cases specifically
         return _generic_matvecmul!(y, 'N', wrap(A, tA), x, MulAddMul(α, β))
@@ -464,14 +473,15 @@ Base.@constprop :aggressive function gemv!(y::StridedVector{Complex{T}}, tA::Abs
     mA == 0 && return y
     nA == 0 && return _rmul_or_fill!(y, β)
     alpha, beta = promote(α, β, zero(T))
+    tA_uc = uppercase(tA) # potentially convert a WrapperChar to a Char
     if alpha isa Union{Bool,T} && beta isa Union{Bool,T} &&
         stride(A, 1) == 1 && abs(stride(A, 2)) >= size(A, 1) &&
-        stride(y, 1) == 1 && tA == 'N' && # reinterpret-based optimization is valid only for contiguous `y`
+        stride(y, 1) == 1 && tA_uc == 'N' && # reinterpret-based optimization is valid only for contiguous `y`
         !iszero(stride(x, 1))
         BLAS.gemv!(tA, alpha, reinterpret(T, A), x, beta, reinterpret(T, y))
         return y
     else
-        Anew, ta = tA in ('S', 's', 'H', 'h') ? (wrap(A, tA), 'N') : (A, tA)
+        Anew, ta = tA_uc in ('S', 'H') ? (wrap(A, tA), oftype(tA, 'N')) : (A, tA)
         return _generic_matvecmul!(y, ta, Anew, x, MulAddMul(α, β))
     end
 end
@@ -487,15 +497,16 @@ Base.@constprop :aggressive function gemv!(y::StridedVector{Complex{T}}, tA::Abs
     mA == 0 && return y
     nA == 0 && return _rmul_or_fill!(y, β)
     alpha, beta = promote(α, β, zero(T))
+    tA_uc = uppercase(tA) # potentially convert a WrapperChar to a Char
     @views if alpha isa Union{Bool,T} && beta isa Union{Bool,T} &&
         stride(A, 1) == 1 && abs(stride(A, 2)) >= size(A, 1) &&
-        !iszero(stride(x, 1)) && tA in ('N', 'T', 'C')
+        !iszero(stride(x, 1)) && tA_uc in ('N', 'T', 'C')
         xfl = reinterpret(reshape, T, x) # Use reshape here.
         yfl = reinterpret(reshape, T, y)
         BLAS.gemv!(tA, alpha, A, xfl[1, :], beta, yfl[1, :])
         BLAS.gemv!(tA, alpha, A, xfl[2, :], beta, yfl[2, :])
         return y
-    elseif tA in ('S', 's', 'H', 'h')
+    elseif tA_uc in ('S', 'H')
         # re-wrap again and use plain ('N') matvec mul algorithm,
         # because _generic_matvecmul! can't handle the HermOrSym cases specifically
         return _generic_matvecmul!(y, 'N', wrap(A, tA), x, MulAddMul(α, β))
@@ -504,10 +515,13 @@ Base.@constprop :aggressive function gemv!(y::StridedVector{Complex{T}}, tA::Abs
     end
 end
 
-function syrk_wrapper!(C::StridedMatrix{T}, tA::AbstractChar, A::StridedVecOrMat{T},
+# the aggressive constprop pushes tA and tB into gemm_wrapper!, which is needed for wrap calls within it
+# to be concretely inferred
+Base.@constprop :aggressive function syrk_wrapper!(C::StridedMatrix{T}, tA::AbstractChar, A::StridedVecOrMat{T},
         _add = MulAddMul()) where {T<:BlasFloat}
     nC = checksquare(C)
-    if tA == 'T'
+    tA_uc = uppercase(tA) # potentially convert a WrapperChar to a Char
+    if tA_uc == 'T'
         (nA, mA) = size(A,1), size(A,2)
         tAt = 'N'
     else
@@ -542,10 +556,13 @@ function syrk_wrapper!(C::StridedMatrix{T}, tA::AbstractChar, A::StridedVecOrMat
     return gemm_wrapper!(C, tA, tAt, A, A, _add)
 end
 
-function herk_wrapper!(C::Union{StridedMatrix{T}, StridedMatrix{Complex{T}}}, tA::AbstractChar, A::Union{StridedVecOrMat{T}, StridedVecOrMat{Complex{T}}},
+# the aggressive constprop pushes tA and tB into gemm_wrapper!, which is needed for wrap calls within it
+# to be concretely inferred
+Base.@constprop :aggressive function herk_wrapper!(C::Union{StridedMatrix{T}, StridedMatrix{Complex{T}}}, tA::AbstractChar, A::Union{StridedVecOrMat{T}, StridedVecOrMat{Complex{T}}},
         _add = MulAddMul()) where {T<:BlasReal}
     nC = checksquare(C)
-    if tA == 'C'
+    tA_uc = uppercase(tA) # potentially convert a WrapperChar to a Char
+    if tA_uc == 'C'
         (nA, mA) = size(A,1), size(A,2)
         tAt = 'N'
     else
@@ -581,20 +598,28 @@ function herk_wrapper!(C::Union{StridedMatrix{T}, StridedMatrix{Complex{T}}}, tA
     return gemm_wrapper!(C, tA, tAt, A, A, _add)
 end
 
-function gemm_wrapper(tA::AbstractChar, tB::AbstractChar,
+# Aggressive constprop helps propagate the values of tA and tB into wrap, which
+# makes the calls concretely inferred
+Base.@constprop :aggressive function gemm_wrapper(tA::AbstractChar, tB::AbstractChar,
                       A::StridedVecOrMat{T},
                       B::StridedVecOrMat{T}) where {T<:BlasFloat}
     mA, nA = lapack_size(tA, A)
     mB, nB = lapack_size(tB, B)
     C = similar(B, T, mA, nB)
-    if all(in(('N', 'T', 'C')), (tA, tB))
+    # We convert the chars to uppercase to potentially unwrap a WrapperChar,
+    # and extract the char corresponding to the wrapper type
+    tA_uc, tB_uc = uppercase(tA), uppercase(tB)
+    # the map in all ensures constprop by acting on tA and tB individually, instead of looping over them.
+    if all(map(in(('N', 'T', 'C')), (tA_uc, tB_uc)))
         gemm_wrapper!(C, tA, tB, A, B)
     else
         _generic_matmatmul!(C, wrap(A, tA), wrap(B, tB), _add)
     end
 end
 
-function gemm_wrapper!(C::StridedVecOrMat{T}, tA::AbstractChar, tB::AbstractChar,
+# Aggressive constprop helps propagate the values of tA and tB into wrap, which
+# makes the calls concretely inferred
+Base.@constprop :aggressive function gemm_wrapper!(C::StridedVecOrMat{T}, tA::AbstractChar, tB::AbstractChar,
                        A::StridedVecOrMat{T}, B::StridedVecOrMat{T},
                        _add = MulAddMul()) where {T<:BlasFloat}
     mA, nA = lapack_size(tA, A)
@@ -634,7 +659,9 @@ function gemm_wrapper!(C::StridedVecOrMat{T}, tA::AbstractChar, tB::AbstractChar
     _generic_matmatmul!(C, wrap(A, tA), wrap(B, tB), _add)
 end
 
-function gemm_wrapper!(C::StridedVecOrMat{Complex{T}}, tA::AbstractChar, tB::AbstractChar,
+# Aggressive constprop helps propagate the values of tA and tB into wrap, which
+# makes the calls concretely inferred
+Base.@constprop :aggressive function gemm_wrapper!(C::StridedVecOrMat{Complex{T}}, tA::AbstractChar, tB::AbstractChar,
                        A::StridedVecOrMat{Complex{T}}, B::StridedVecOrMat{T},
                        _add = MulAddMul()) where {T<:BlasReal}
     mA, nA = lapack_size(tA, A)
@@ -664,13 +691,15 @@ function gemm_wrapper!(C::StridedVecOrMat{Complex{T}}, tA::AbstractChar, tB::Abs
 
     alpha, beta = promote(_add.alpha, _add.beta, zero(T))
 
+    tA_uc = uppercase(tA) # potentially convert a WrapperChar to a Char
+
     # Make-sure reinterpret-based optimization is BLAS-compatible.
     if (alpha isa Union{Bool,T} &&
         beta isa Union{Bool,T} &&
         stride(A, 1) == stride(B, 1) == stride(C, 1) == 1 &&
         stride(A, 2) >= size(A, 1) &&
         stride(B, 2) >= size(B, 1) &&
-        stride(C, 2) >= size(C, 1) && tA == 'N')
+        stride(C, 2) >= size(C, 1) && tA_uc == 'N')
         BLAS.gemm!(tA, tB, alpha, reinterpret(T, A), B, beta, reinterpret(T, C))
         return C
     end
@@ -703,9 +732,10 @@ parameters must satisfy `length(ir_dest) == length(ir_src)` and
 See also [`copy_transpose!`](@ref) and [`copy_adjoint!`](@ref).
 """
 function copyto!(B::AbstractVecOrMat, ir_dest::AbstractUnitRange{Int}, jr_dest::AbstractUnitRange{Int}, tM::AbstractChar, M::AbstractVecOrMat, ir_src::AbstractUnitRange{Int}, jr_src::AbstractUnitRange{Int})
-    if tM == 'N'
+    tM_uc = uppercase(tM) # potentially convert a WrapperChar to a Char
+    if tM_uc == 'N'
         copyto!(B, ir_dest, jr_dest, M, ir_src, jr_src)
-    elseif tM == 'T'
+    elseif tM_uc == 'T'
         copy_transpose!(B, ir_dest, jr_dest, M, jr_src, ir_src)
     else
         copy_adjoint!(B, ir_dest, jr_dest, M, jr_src, ir_src)
@@ -734,11 +764,12 @@ range parameters must satisfy `length(ir_dest) == length(jr_src)` and
 See also [`copyto!`](@ref) and [`copy_adjoint!`](@ref).
 """
 function copy_transpose!(B::AbstractMatrix, ir_dest::AbstractUnitRange{Int}, jr_dest::AbstractUnitRange{Int}, tM::AbstractChar, M::AbstractVecOrMat, ir_src::AbstractUnitRange{Int}, jr_src::AbstractUnitRange{Int})
-    if tM == 'N'
+    tM_uc = uppercase(tM) # potentially convert a WrapperChar to a Char
+    if tM_uc == 'N'
         copy_transpose!(B, ir_dest, jr_dest, M, ir_src, jr_src)
     else
         copyto!(B, ir_dest, jr_dest, M, jr_src, ir_src)
-        tM == 'C' && conj!(@view B[ir_dest, jr_dest])
+        tM_uc == 'C' && conj!(@view B[ir_dest, jr_dest])
     end
     B
 end
@@ -751,7 +782,8 @@ end
 
 @inline function generic_matvecmul!(C::AbstractVector, tA, A::AbstractVecOrMat, B::AbstractVector,
                                     _add::MulAddMul = MulAddMul())
-    Anew, ta = tA in ('S', 's', 'H', 'h') ? (wrap(A, tA), 'N') : (A, tA)
+    tA_uc = uppercase(tA) # potentially convert a WrapperChar to a Char
+    Anew, ta = tA_uc in ('S', 'H') ? (wrap(A, tA), oftype(tA, 'N')) : (A, tA)
     return _generic_matvecmul!(C, ta, Anew, B, _add)
 end
 
diff --git a/stdlib/LinearAlgebra/test/matmul.jl b/stdlib/LinearAlgebra/test/matmul.jl
index c760f1adeffdd0..db61fbe0ab45ab 100644
--- a/stdlib/LinearAlgebra/test/matmul.jl
+++ b/stdlib/LinearAlgebra/test/matmul.jl
@@ -30,6 +30,30 @@ mul_wrappers = [
     h(A) = LinearAlgebra.wrap(LinearAlgebra._unwrap(A), LinearAlgebra.wrapper_char(A))
     @test @inferred(h(transpose(A))) === transpose(A)
     @test @inferred(h(adjoint(A))) === transpose(A)
+
+    M = rand(2,2)
+    for S in (Symmetric(M), Hermitian(M))
+        @test @inferred((A -> LinearAlgebra.wrap(parent(A), LinearAlgebra.wrapper_char(A)))(S)) === Symmetric(M)
+    end
+    M = rand(ComplexF64,2,2)
+    for S in (Symmetric(M), Hermitian(M))
+        @test @inferred((A -> LinearAlgebra.wrap(parent(A), LinearAlgebra.wrapper_char(A)))(S)) === S
+    end
+
+    @testset "WrapperChar" begin
+        @test LinearAlgebra.WrapperChar('c') == 'c'
+        @test LinearAlgebra.WrapperChar('C') == 'C'
+        @testset "constant propagation in uppercase/lowercase" begin
+            v = @inferred (() -> Val(uppercase(LinearAlgebra.WrapperChar('C'))))()
+            @test v isa Val{'C'}
+            v = @inferred (() -> Val(uppercase(LinearAlgebra.WrapperChar('s'))))()
+            @test v isa Val{'S'}
+            v = @inferred (() -> Val(lowercase(LinearAlgebra.WrapperChar('C'))))()
+            @test v isa Val{'c'}
+            v = @inferred (() -> Val(lowercase(LinearAlgebra.WrapperChar('s'))))()
+            @test v isa Val{'s'}
+        end
+    end
 end
 
 @testset "matrices with zero dimensions" begin