Rename ctranspose to adjoint

NEWS.md

@@ -309,6 +309,9 @@ Deprecated or removed
   * `Base.cpad` has been removed; use an appropriate combination of `rpad` and `lpad`
     instead ([#23187]).
 
+  * `ctranspose` and `ctranspose!` have been deprecated in favor of `adjoint` and `adjoint!`,
+    respectively.
+
 Julia v0.6.0 Release Notes
 ==========================
 

base/deprecated.jl

@@ -1422,7 +1422,7 @@ end
 module Operators
     for op in [:!, :(!=), :(!==), :%, :&, :*, :+, :-, :/, ://, :<, :<:, :<<, :(<=),
                :<|, :(==), :(===), :>, :>:, :(>=), :>>, :>>>, :\, :^, :colon,
-               :ctranspose, :getindex, :hcat, :hvcat, :setindex!, :transpose, :vcat,
+               :adjoint, :getindex, :hcat, :hvcat, :setindex!, :transpose, :vcat,
                :xor, :|, :|>, :~, :×, :÷, :∈, :∉, :∋, :∌, :∘, :√, :∛, :∩, :∪, :≠, :≤,
                :≥, :⊆, :⊈, :⊊, :⊻, :⋅]
         if isdefined(Base, op)
@@ -1684,6 +1684,10 @@ end
 # PR #22742: change in isapprox semantics
 @deprecate rtoldefault(x,y) rtoldefault(x,y,0) false
 
+# PR #23235
+@deprecate ctranspose adjoint
+@deprecate ctranspose! adjoint
+
 # END 0.7 deprecations
 
 # BEGIN 1.0 deprecations

base/exports.jl

@@ -562,8 +562,8 @@ export
     cond,
     condskeel,
     cross,
-    ctranspose!,
-    ctranspose,
+    adjoint!,
+    adjoint,
     det,
     diag,
     diagind,

base/linalg/bidiag.jl

@@ -221,7 +221,7 @@ broadcast(::typeof(floor), ::Type{T}, M::Bidiagonal) where {T<:Integer} = Bidiag
 broadcast(::typeof(ceil), ::Type{T}, M::Bidiagonal) where {T<:Integer} = Bidiagonal(ceil.(T, M.dv), ceil.(T, M.ev), M.uplo)
 
 transpose(M::Bidiagonal) = Bidiagonal(M.dv, M.ev, M.uplo == 'U' ? :L : :U)
-ctranspose(M::Bidiagonal) = Bidiagonal(conj(M.dv), conj(M.ev), M.uplo == 'U' ? :L : :U)
+adjoint(M::Bidiagonal) = Bidiagonal(conj(M.dv), conj(M.ev), M.uplo == 'U' ? :L : :U)
 
 istriu(M::Bidiagonal) = M.uplo == 'U' || iszero(M.ev)
 istril(M::Bidiagonal) = M.uplo == 'L' || iszero(M.ev)
@@ -456,7 +456,7 @@ end
 #Linear solvers
 A_ldiv_B!(A::Union{Bidiagonal, AbstractTriangular}, b::AbstractVector) = naivesub!(A, b)
 At_ldiv_B!(A::Bidiagonal, b::AbstractVector) = A_ldiv_B!(transpose(A), b)
-Ac_ldiv_B!(A::Bidiagonal, b::AbstractVector) = A_ldiv_B!(ctranspose(A), b)
+Ac_ldiv_B!(A::Bidiagonal, b::AbstractVector) = A_ldiv_B!(adjoint(A), b)
 function A_ldiv_B!(A::Union{Bidiagonal,AbstractTriangular}, B::AbstractMatrix)
     nA,mA = size(A)
     tmp = similar(B,size(B,1))

base/linalg/bitarray.jl

@@ -295,4 +295,4 @@ function transpose(B::BitMatrix)
     return Bt
 end
 
-ctranspose(B::Union{BitMatrix,BitVector}) = transpose(B)
+adjoint(B::Union{BitMatrix,BitVector}) = transpose(B)

base/linalg/cholesky.jl

@@ -150,7 +150,7 @@ function chol(A::RealHermSymComplexHerm)
     if A.uplo == 'U'
         copy!(AA, A.data)
     else
-        Base.ctranspose!(AA, A.data)
+        Base.adjoint!(AA, A.data)
     end
     chol!(Hermitian(AA, :U))
 end

base/linalg/conjarray.jl

@@ -5,7 +5,7 @@
 
 A lazy-view wrapper of an `AbstractArray`, taking the elementwise complex conjugate. This
 type is usually constructed (and unwrapped) via the [`conj`](@ref) function (or related
-[`ctranspose`](@ref)), but currently this is the default behavior for `RowVector` only. For
+[`adjoint`](@ref)), but currently this is the default behavior for `RowVector` only. For
 other arrays, the `ConjArray` constructor can be used directly.
 
 # Examples

base/linalg/diagonal.jl

@@ -186,11 +186,11 @@ function A_mul_B!(D::Diagonal, B::UnitUpperTriangular)
     UpperTriangular(B.data)
 end
 
-Ac_mul_B(D::Diagonal, B::Diagonal) = Diagonal(ctranspose.(D.diag) .* B.diag)
-Ac_mul_B(A::AbstractTriangular, D::Diagonal) = A_mul_B!(ctranspose(A), D)
+Ac_mul_B(D::Diagonal, B::Diagonal) = Diagonal(adjoint.(D.diag) .* B.diag)
+Ac_mul_B(A::AbstractTriangular, D::Diagonal) = A_mul_B!(adjoint(A), D)
 function Ac_mul_B(A::AbstractMatrix, D::Diagonal)
     Ac = similar(A, promote_op(*, eltype(A), eltype(D.diag)), (size(A, 2), size(A, 1)))
-    ctranspose!(Ac, A)
+    adjoint!(Ac, A)
     A_mul_B!(Ac, D)
 end
 
@@ -202,12 +202,12 @@ function At_mul_B(A::AbstractMatrix, D::Diagonal)
     A_mul_B!(At, D)
 end
 
-A_mul_Bc(D::Diagonal, B::Diagonal) = Diagonal(D.diag .* ctranspose.(B.diag))
-A_mul_Bc(D::Diagonal, B::AbstractTriangular) = A_mul_B!(D, ctranspose(B))
+A_mul_Bc(D::Diagonal, B::Diagonal) = Diagonal(D.diag .* adjoint.(B.diag))
+A_mul_Bc(D::Diagonal, B::AbstractTriangular) = A_mul_B!(D, adjoint(B))
 A_mul_Bc(D::Diagonal, Q::Union{Base.LinAlg.QRCompactWYQ,Base.LinAlg.QRPackedQ}) = A_mul_Bc!(Array(D), Q)
 function A_mul_Bc(D::Diagonal, A::AbstractMatrix)
     Ac = similar(A, promote_op(*, eltype(A), eltype(D.diag)), (size(A, 2), size(A, 1)))
-    ctranspose!(Ac, A)
+    adjoint!(Ac, A)
     A_mul_B!(D, Ac)
 end
 
@@ -219,7 +219,7 @@ function A_mul_Bt(D::Diagonal, A::AbstractMatrix)
     A_mul_B!(D, At)
 end
 
-Ac_mul_Bc(D::Diagonal, B::Diagonal) = Diagonal(ctranspose.(D.diag) .* ctranspose.(B.diag))
+Ac_mul_Bc(D::Diagonal, B::Diagonal) = Diagonal(adjoint.(D.diag) .* adjoint.(B.diag))
 At_mul_Bt(D::Diagonal, B::Diagonal) = Diagonal(transpose.(D.diag) .* transpose.(B.diag))
 
 A_mul_B!(A::Diagonal,B::Diagonal)  = throw(MethodError(A_mul_B!, Tuple{Diagonal,Diagonal}))
@@ -235,11 +235,11 @@ A_mul_Bc!(A::AbstractMatrix,B::Diagonal) = scale!(A,conj(B.diag))
 
 # Get ambiguous method if try to unify AbstractVector/AbstractMatrix here using AbstractVecOrMat
 A_mul_B!(out::AbstractVector, A::Diagonal, in::AbstractVector) = out .= A.diag .* in
-Ac_mul_B!(out::AbstractVector, A::Diagonal, in::AbstractVector) = out .= ctranspose.(A.diag) .* in
+Ac_mul_B!(out::AbstractVector, A::Diagonal, in::AbstractVector) = out .= adjoint.(A.diag) .* in
 At_mul_B!(out::AbstractVector, A::Diagonal, in::AbstractVector) = out .= transpose.(A.diag) .* in
 
 A_mul_B!(out::AbstractMatrix, A::Diagonal, in::AbstractMatrix) = out .= A.diag .* in
-Ac_mul_B!(out::AbstractMatrix, A::Diagonal, in::AbstractMatrix) = out .= ctranspose.(A.diag) .* in
+Ac_mul_B!(out::AbstractMatrix, A::Diagonal, in::AbstractMatrix) = out .= adjoint.(A.diag) .* in
 At_mul_B!(out::AbstractMatrix, A::Diagonal, in::AbstractMatrix) = out .= transpose.(A.diag) .* in
 
 # ambiguities with Symmetric/Hermitian
@@ -306,13 +306,13 @@ A_rdiv_Bt!(A::AbstractMatrix{T}, D::Diagonal{T}) where {T} = A_rdiv_B!(A, D)
 # Methods to resolve ambiguities with `Diagonal`
 @inline *(rowvec::RowVector, D::Diagonal) = transpose(D * transpose(rowvec))
 @inline A_mul_Bt(D::Diagonal, rowvec::RowVector) = D*transpose(rowvec)
-@inline A_mul_Bc(D::Diagonal, rowvec::RowVector) = D*ctranspose(rowvec)
+@inline A_mul_Bc(D::Diagonal, rowvec::RowVector) = D*adjoint(rowvec)
 
 conj(D::Diagonal) = Diagonal(conj(D.diag))
 transpose(D::Diagonal{<:Number}) = D
 transpose(D::Diagonal) = Diagonal(transpose.(D.diag))
-ctranspose(D::Diagonal{<:Number}) = conj(D)
-ctranspose(D::Diagonal) = Diagonal(ctranspose.(D.diag))
+adjoint(D::Diagonal{<:Number}) = conj(D)
+adjoint(D::Diagonal) = Diagonal(adjoint.(D.diag))
 
 diag(D::Diagonal) = D.diag
 trace(D::Diagonal) = sum(D.diag)

base/linalg/factorization.jl

@@ -6,7 +6,7 @@ abstract type Factorization{T} end
 
 eltype(::Type{Factorization{T}}) where {T} = T
 transpose(F::Factorization) = error("transpose not implemented for $(typeof(F))")
-ctranspose(F::Factorization) = error("ctranspose not implemented for $(typeof(F))")
+adjoint(F::Factorization) = error("adjoint not implemented for $(typeof(F))")
 
 macro assertposdef(A, info)
    :($(esc(info)) == 0 ? $(esc(A)) : throw(PosDefException($(esc(info)))))

base/linalg/generic.jl

@@ -942,7 +942,7 @@ function ishermitian(A::AbstractMatrix)
         return false
     end
     for i = indsn, j = i:last(indsn)
-        if A[i,j] != ctranspose(A[j,i])
+        if A[i,j] != adjoint(A[j,i])
             return false
         end
     end

base/linalg/givens.jl

@@ -41,8 +41,8 @@ convert(::Type{Rotation{T}}, R::Rotation) where {T} = Rotation{T}([convert(Given
 convert(::Type{AbstractRotation{T}}, G::Givens) where {T} = convert(Givens{T}, G)
 convert(::Type{AbstractRotation{T}}, R::Rotation) where {T} = convert(Rotation{T}, R)
 
-ctranspose(G::Givens) = Givens(G.i1, G.i2, conj(G.c), -G.s)
-ctranspose(R::Rotation{T}) where {T} = Rotation{T}(reverse!([ctranspose(r) for r in R.rotations]))
+adjoint(G::Givens) = Givens(G.i1, G.i2, conj(G.c), -G.s)
+adjoint(R::Rotation{T}) where {T} = Rotation{T}(reverse!([adjoint(r) for r in R.rotations]))
 
 realmin2(::Type{Float32}) = reinterpret(Float32, 0x26000000)
 realmin2(::Type{Float64}) = reinterpret(Float64, 0x21a0000000000000)

base/linalg/linalg.jl

@@ -6,7 +6,7 @@ import Base: \, /, *, ^, +, -, ==
 import Base: A_mul_Bt, At_ldiv_Bt, A_rdiv_Bc, At_ldiv_B, Ac_mul_Bc, A_mul_Bc, Ac_mul_B,
     Ac_ldiv_B, Ac_ldiv_Bc, At_mul_Bt, A_rdiv_Bt, At_mul_B
 import Base: USE_BLAS64, abs, big, broadcast, ceil, conj, convert, copy, copy!,
-    ctranspose, eltype, eye, findmax, findmin, fill!, floor, full, getindex,
+    adjoint, eltype, eye, findmax, findmin, fill!, floor, full, getindex,
     hcat, imag, indices, inv, isapprox, isone, IndexStyle, kron, length, map,
     ndims, oneunit, parent, power_by_squaring, print_matrix, promote_rule, real, round,
     setindex!, show, similar, size, transpose, trunc, typed_hcat
@@ -63,8 +63,8 @@ export
     copy!,
     copy_transpose!,
     cross,
-    ctranspose,
-    ctranspose!,
+    adjoint,
+    adjoint!,
     det,
     diag,
     diagind,

base/linalg/lq.jl

@@ -56,7 +56,7 @@ convert(::Type{Matrix}, A::LQ) = convert(Array, convert(AbstractArray, A))
 convert(::Type{Array}, A::LQ) = convert(Matrix, A)
 full(A::LQ) = convert(AbstractArray, A)
 
-ctranspose(A::LQ{T}) where {T} = QR{T,typeof(A.factors)}(A.factors', A.τ)
+adjoint(A::LQ{T}) where {T} = QR{T,typeof(A.factors)}(A.factors', A.τ)
 
 function getindex(A::LQ, d::Symbol)
     m, n = size(A)
@@ -164,7 +164,7 @@ for (f1, f2) in ((:A_mul_Bc, :A_mul_B!),
         function ($f1)(A::LQPackedQ, B::StridedVecOrMat)
             TAB = promote_type(eltype(A), eltype(B))
             BB = similar(B, TAB, (size(B, 2), size(B, 1)))
-            ctranspose!(BB, B)
+            adjoint!(BB, B)
             return ($f2)(A, BB)
         end
     end
@@ -198,7 +198,7 @@ for (f1, f2) in ((:Ac_mul_B, :A_mul_B!),
         function ($f1)(A::StridedMatrix, B::LQPackedQ)
             TAB = promote_type(eltype(A), eltype(B))
             AA = similar(A, TAB, (size(A, 2), size(A, 1)))
-            ctranspose!(AA, A)
+            adjoint!(AA, A)
             return ($f2)(AA, B)
         end
     end

base/linalg/lu.jl

@@ -275,8 +275,8 @@ At_ldiv_Bt(A::LU{T,<:StridedMatrix}, B::StridedVecOrMat{T}) where {T<:BlasFloat}
 At_ldiv_Bt(A::LU, B::StridedVecOrMat) = At_ldiv_B(A, transpose(B))
 
 Ac_ldiv_Bc(A::LU{T,<:StridedMatrix}, B::StridedVecOrMat{T}) where {T<:BlasComplex} =
-    @assertnonsingular LAPACK.getrs!('C', A.factors, A.ipiv, ctranspose(B)) A.info
-Ac_ldiv_Bc(A::LU, B::StridedVecOrMat) = Ac_ldiv_B(A, ctranspose(B))
+    @assertnonsingular LAPACK.getrs!('C', A.factors, A.ipiv, adjoint(B)) A.info
+Ac_ldiv_Bc(A::LU, B::StridedVecOrMat) = Ac_ldiv_B(A, adjoint(B))
 
 function det(F::LU{T}) where T
     n = checksquare(F)

base/linalg/matmul.jl

@@ -663,14 +663,14 @@ function matmul2x2!(C::AbstractMatrix, tA, tB, A::AbstractMatrix, B::AbstractMat
     if tA == 'T'
         A11 = transpose(A[1,1]); A12 = transpose(A[2,1]); A21 = transpose(A[1,2]); A22 = transpose(A[2,2])
     elseif tA == 'C'
-        A11 = ctranspose(A[1,1]); A12 = ctranspose(A[2,1]); A21 = ctranspose(A[1,2]); A22 = ctranspose(A[2,2])
+        A11 = adjoint(A[1,1]); A12 = adjoint(A[2,1]); A21 = adjoint(A[1,2]); A22 = adjoint(A[2,2])
     else
         A11 = A[1,1]; A12 = A[1,2]; A21 = A[2,1]; A22 = A[2,2]
     end
     if tB == 'T'
         B11 = transpose(B[1,1]); B12 = transpose(B[2,1]); B21 = transpose(B[1,2]); B22 = transpose(B[2,2])
     elseif tB == 'C'
-        B11 = ctranspose(B[1,1]); B12 = ctranspose(B[2,1]); B21 = ctranspose(B[1,2]); B22 = ctranspose(B[2,2])
+        B11 = adjoint(B[1,1]); B12 = adjoint(B[2,1]); B21 = adjoint(B[1,2]); B22 = adjoint(B[2,2])
     else
         B11 = B[1,1]; B12 = B[1,2]; B21 = B[2,1]; B22 = B[2,2]
     end
@@ -697,9 +697,9 @@ function matmul3x3!(C::AbstractMatrix, tA, tB, A::AbstractMatrix, B::AbstractMat
         A21 = transpose(A[1,2]); A22 = transpose(A[2,2]); A23 = transpose(A[3,2])
         A31 = transpose(A[1,3]); A32 = transpose(A[2,3]); A33 = transpose(A[3,3])
     elseif tA == 'C'
-        A11 = ctranspose(A[1,1]); A12 = ctranspose(A[2,1]); A13 = ctranspose(A[3,1])
-        A21 = ctranspose(A[1,2]); A22 = ctranspose(A[2,2]); A23 = ctranspose(A[3,2])
-        A31 = ctranspose(A[1,3]); A32 = ctranspose(A[2,3]); A33 = ctranspose(A[3,3])
+        A11 = adjoint(A[1,1]); A12 = adjoint(A[2,1]); A13 = adjoint(A[3,1])
+        A21 = adjoint(A[1,2]); A22 = adjoint(A[2,2]); A23 = adjoint(A[3,2])
+        A31 = adjoint(A[1,3]); A32 = adjoint(A[2,3]); A33 = adjoint(A[3,3])
     else
         A11 = A[1,1]; A12 = A[1,2]; A13 = A[1,3]
         A21 = A[2,1]; A22 = A[2,2]; A23 = A[2,3]
@@ -711,9 +711,9 @@ function matmul3x3!(C::AbstractMatrix, tA, tB, A::AbstractMatrix, B::AbstractMat
         B21 = transpose(B[1,2]); B22 = transpose(B[2,2]); B23 = transpose(B[3,2])
         B31 = transpose(B[1,3]); B32 = transpose(B[2,3]); B33 = transpose(B[3,3])
     elseif tB == 'C'
-        B11 = ctranspose(B[1,1]); B12 = ctranspose(B[2,1]); B13 = ctranspose(B[3,1])
-        B21 = ctranspose(B[1,2]); B22 = ctranspose(B[2,2]); B23 = ctranspose(B[3,2])
-        B31 = ctranspose(B[1,3]); B32 = ctranspose(B[2,3]); B33 = ctranspose(B[3,3])
+        B11 = adjoint(B[1,1]); B12 = adjoint(B[2,1]); B13 = adjoint(B[3,1])
+        B21 = adjoint(B[1,2]); B22 = adjoint(B[2,2]); B23 = adjoint(B[3,2])
+        B31 = adjoint(B[1,3]); B32 = adjoint(B[2,3]); B33 = adjoint(B[3,3])
     else
         B11 = B[1,1]; B12 = B[1,2]; B13 = B[1,3]
         B21 = B[2,1]; B22 = B[2,2]; B23 = B[2,3]

base/linalg/qr.jl

@@ -595,7 +595,7 @@ for (f1, f2) in ((:A_mul_Bc, :A_mul_B!),
         function ($f1)(Q::AbstractQ, B::StridedVecOrMat)
             TQB = promote_type(eltype(Q), eltype(B))
             Bc = similar(B, TQB, (size(B, 2), size(B, 1)))
-            ctranspose!(Bc, B)
+            adjoint!(Bc, B)
             return ($f2)(convert(AbstractMatrix{TQB}, Q), Bc)
         end
     end
@@ -678,7 +678,7 @@ function A_mul_Bc(A::StridedMatrix, B::AbstractQ)
         throw(DimensionMismatch("matrix A has dimensions $(size(A)) but matrix B has dimensions $(size(B))"))
     end
 end
-@inline A_mul_Bc(rowvec::RowVector, B::AbstractQ) = ctranspose(B*ctranspose(rowvec))
+@inline A_mul_Bc(rowvec::RowVector, B::AbstractQ) = adjoint(B*adjoint(rowvec))
 
 
 ### AcQ/AcQc
@@ -688,7 +688,7 @@ for (f1, f2) in ((:Ac_mul_B, :A_mul_B!),
         function ($f1)(A::StridedVecOrMat, Q::AbstractQ)
             TAQ = promote_type(eltype(A), eltype(Q))
             Ac = similar(A, TAQ, (size(A, 2), size(A, 1)))
-            ctranspose!(Ac, A)
+            adjoint!(Ac, A)
             return ($f2)(Ac, convert(AbstractMatrix{TAQ}, Q))
         end
     end

base/linalg/rowvector.jl

@@ -6,7 +6,7 @@
 A lazy-view wrapper of an [`AbstractVector`](@ref), which turns a length-`n` vector into a `1×n`
 shaped row vector and represents the transpose of a vector (the elements are also transposed
 recursively). This type is usually constructed (and unwrapped) via the [`transpose`](@ref)
-function or `.'` operator (or related [`ctranspose`](@ref) or `'` operator).
+function or `.'` operator (or related [`adjoint`](@ref) or `'` operator).
 
 By convention, a vector can be multiplied by a matrix on its left (`A * v`) whereas a row
 vector can be multiplied by a matrix on its right (such that `v.' * A = (A.' * v).'`). It
@@ -75,12 +75,12 @@ julia> transpose(v)
 ```
 """
 @inline transpose(vec::AbstractVector) = RowVector(vec)
-@inline ctranspose(vec::AbstractVector) = RowVector(_conj(vec))
+@inline adjoint(vec::AbstractVector) = RowVector(_conj(vec))
 
 @inline transpose(rowvec::RowVector) = rowvec.vec
 @inline transpose(rowvec::ConjRowVector) = copy(rowvec.vec) # remove the ConjArray wrapper from any raw vector
-@inline ctranspose(rowvec::RowVector) = conj(rowvec.vec)
-@inline ctranspose(rowvec::RowVector{<:Real}) = rowvec.vec
+@inline adjoint(rowvec::RowVector) = conj(rowvec.vec)
+@inline adjoint(rowvec::RowVector{<:Real}) = rowvec.vec
 
 parent(rowvec::RowVector) = rowvec.vec
 
@@ -208,24 +208,24 @@ At_mul_B(vec::AbstractVector, rowvec::RowVector) = throw(DimensionMismatch(
 
 # Conjugated forms
 A_mul_Bc(::RowVector, ::AbstractVector) = throw(DimensionMismatch("Cannot multiply two transposed vectors"))
-@inline A_mul_Bc(rowvec::RowVector, mat::AbstractMatrix) = ctranspose(mat * ctranspose(rowvec))
-@inline A_mul_Bc(rowvec1::RowVector, rowvec2::RowVector) = rowvec1 * ctranspose(rowvec2)
+@inline A_mul_Bc(rowvec::RowVector, mat::AbstractMatrix) = adjoint(mat * adjoint(rowvec))
+@inline A_mul_Bc(rowvec1::RowVector, rowvec2::RowVector) = rowvec1 * adjoint(rowvec2)
 A_mul_Bc(vec::AbstractVector, rowvec::RowVector) = throw(DimensionMismatch("Cannot multiply two vectors"))
-@inline A_mul_Bc(vec1::AbstractVector, vec2::AbstractVector) = vec1 * ctranspose(vec2)
-@inline A_mul_Bc(mat::AbstractMatrix, rowvec::RowVector) = mat * ctranspose(rowvec)
+@inline A_mul_Bc(vec1::AbstractVector, vec2::AbstractVector) = vec1 * adjoint(vec2)
+@inline A_mul_Bc(mat::AbstractMatrix, rowvec::RowVector) = mat * adjoint(rowvec)
 
-@inline Ac_mul_Bc(rowvec::RowVector, vec::AbstractVector) = ctranspose(rowvec) * ctranspose(vec)
-@inline Ac_mul_Bc(vec::AbstractVector, mat::AbstractMatrix) = ctranspose(mat * vec)
+@inline Ac_mul_Bc(rowvec::RowVector, vec::AbstractVector) = adjoint(rowvec) * adjoint(vec)
+@inline Ac_mul_Bc(vec::AbstractVector, mat::AbstractMatrix) = adjoint(mat * vec)
 Ac_mul_Bc(rowvec1::RowVector, rowvec2::RowVector) = throw(DimensionMismatch("Cannot multiply two vectors"))
-@inline Ac_mul_Bc(vec::AbstractVector, rowvec::RowVector) = ctranspose(vec)*ctranspose(rowvec)
+@inline Ac_mul_Bc(vec::AbstractVector, rowvec::RowVector) = adjoint(vec)*adjoint(rowvec)
 Ac_mul_Bc(vec::AbstractVector, rowvec::AbstractVector) = throw(DimensionMismatch("Cannot multiply two transposed vectors"))
-@inline Ac_mul_Bc(mat::AbstractMatrix, rowvec::RowVector) = mat' * ctranspose(rowvec)
+@inline Ac_mul_Bc(mat::AbstractMatrix, rowvec::RowVector) = mat' * adjoint(rowvec)
 
 Ac_mul_B(::RowVector, ::AbstractVector) = throw(DimensionMismatch("Cannot multiply two vectors"))
-@inline Ac_mul_B(vec::AbstractVector, mat::AbstractMatrix) = ctranspose(Ac_mul_B(mat,vec))
-@inline Ac_mul_B(rowvec1::RowVector, rowvec2::RowVector) = ctranspose(rowvec1) * rowvec2
+@inline Ac_mul_B(vec::AbstractVector, mat::AbstractMatrix) = adjoint(Ac_mul_B(mat,vec))
+@inline Ac_mul_B(rowvec1::RowVector, rowvec2::RowVector) = adjoint(rowvec1) * rowvec2
 Ac_mul_B(vec::AbstractVector, rowvec::RowVector) = throw(DimensionMismatch("Cannot multiply two transposed vectors"))
-@inline Ac_mul_B(vec1::AbstractVector, vec2::AbstractVector) = ctranspose(vec1)*vec2
+@inline Ac_mul_B(vec1::AbstractVector, vec2::AbstractVector) = adjoint(vec1)*vec2
 
 # Left Division #
 
@@ -237,4 +237,4 @@ Ac_ldiv_B(mat::AbstractMatrix, rowvec::RowVector) = throw(DimensionMismatch("Can
 
 @inline /(rowvec::RowVector, mat::AbstractMatrix) = transpose(transpose(mat) \ transpose(rowvec))
 @inline A_rdiv_Bt(rowvec::RowVector, mat::AbstractMatrix) = transpose(mat \ transpose(rowvec))
-@inline A_rdiv_Bc(rowvec::RowVector, mat::AbstractMatrix) = ctranspose(mat  \ ctranspose(rowvec))
+@inline A_rdiv_Bc(rowvec::RowVector, mat::AbstractMatrix) = adjoint(mat  \ adjoint(rowvec))