Added function to compute Diagonal*F.Q' and faster methods for other variants.

stdlib/LinearAlgebra/src/diagonal.jl

@@ -289,7 +289,8 @@ function *(transA::Transpose{<:Any,<:AbstractMatrix}, D::Diagonal)
     rmul!(At, D)
 end
 
-*(D::Diagonal, adjQ::Adjoint{<:Any,<:Union{QRCompactWYQ,QRPackedQ}}) = (Q = adjQ.parent; rmul!(Array(D), adjoint(Q)))
+*(D::Diagonal, adjQ::Adjoint{<:Any,<:Union{QRCompactWYQ,QRPackedQ}}) = rmul!(Array{promote_type(eltype(D), eltype(adjQ))}(D), adjQ)
+
 function *(D::Diagonal, adjA::Adjoint{<:Any,<:AbstractMatrix})
     A = adjA.parent
     Ac = similar(A, promote_op(*, eltype(A), eltype(D.diag)), (size(A, 2), size(A, 1)))

stdlib/LinearAlgebra/src/special.jl

@@ -284,6 +284,12 @@ rmul!(A::AbstractTriangular, adjB::Adjoint{<:Any,<:Union{QRCompactWYQ,QRPackedQ}
     (B = adjB.parent; rmul!(full!(A), adjoint(B)))
 *(A::AbstractTriangular, adjB::Adjoint{<:Any,<:Union{QRCompactWYQ,QRPackedQ}}) =
     (B = adjB.parent; *(copyto!(similar(parent(A)), A), adjoint(B)))
+*(A::BiTriSym, adjB::Adjoint{<:Any,<:Union{QRCompactWYQ, QRPackedQ}}) =
+    rmul!(copyto!(Array{promote_type(eltype(A), eltype(adjB))}(undef, size(A)...), A), adjB)
+*(adjA::Adjoint{<:Any,<:Union{QRCompactWYQ, QRPackedQ}}, B::Diagonal) =
+    lmul!(adjA, copyto!(Array{promote_type(eltype(adjA), eltype(B))}(undef, size(B)...), B))
+*(adjA::Adjoint{<:Any,<:Union{QRCompactWYQ, QRPackedQ}}, B::BiTriSym) =
+    lmul!(adjA, copyto!(Array{promote_type(eltype(adjA), eltype(B))}(undef, size(B)...), B))
 
 # fill[stored]! methods
 fillstored!(A::Diagonal, x) = (fill!(A.diag, x); A)

stdlib/LinearAlgebra/test/qr.jl

@@ -407,4 +407,11 @@ end
     end
 end
 
+@testset "issue #38974" begin
+    A = qr(ones(3, 1))
+    B = I(3)
+    C = B*A.Q'
+    @test C ≈ A.Q
+end
+
 end # module TestQR

stdlib/LinearAlgebra/test/special.jl

@@ -434,4 +434,17 @@ end
     end
 end
 
+@testset "BiTriSym*Q' and Q'*BiTriSym" begin
+    dl = [1, 1, 1];
+    d = [1, 1, 1, 1];
+    Tri = Tridiagonal(dl, d, dl)
+    Bi = Bidiagonal(d, dl, :L)
+    Sym = SymTridiagonal(d, dl)
+    F = qr(ones(4, 1))
+    A=F.Q'
+    @test Tri*A ≈ (A*Tri)'
+    @test Bi*A ≈ (A'*Bi')'
+    @test Sym*A ≈ (A*Sym)'
+end
+
 end # module TestSpecial