diff --git a/stdlib/LinearAlgebra/src/bidiag.jl b/stdlib/LinearAlgebra/src/bidiag.jl
index 243553ebc64c6..b50b004ac9584 100644
--- a/stdlib/LinearAlgebra/src/bidiag.jl
+++ b/stdlib/LinearAlgebra/src/bidiag.jl
@@ -165,29 +165,34 @@ function Base.replace_in_print_matrix(A::Bidiagonal,i::Integer,j::Integer,s::Abs
 end
 
 #Converting from Bidiagonal to dense Matrix
-function Matrix{T}(A::Bidiagonal) where T
-    n = size(A, 1)
-    B = zeros(T, n, n)
-    if n == 0
-        return B
-    end
-    for i = 1:n - 1
-        B[i,i] = A.dv[i]
-        if A.uplo == 'U'
-            B[i, i + 1] = A.ev[i]
-        else
-            B[i + 1, i] = A.ev[i]
-        end
-    end
-    B[n,n] = A.dv[n]
-    return B
-end
+Matrix{T}(A::Bidiagonal) where {T} = copyto!(Matrix{T}(undef, size(A)), A)
 Matrix(A::Bidiagonal{T}) where {T} = Matrix{T}(A)
 Array(A::Bidiagonal) = Matrix(A)
 promote_rule(::Type{Matrix{T}}, ::Type{<:Bidiagonal{S}}) where {T,S} =
     @isdefined(T) && @isdefined(S) ? Matrix{promote_type(T,S)} : Matrix
 promote_rule(::Type{Matrix}, ::Type{<:Bidiagonal}) = Matrix
 
+function copyto!(A::AbstractMatrix{T}, B::Bidiagonal) where {T}
+    require_one_based_indexing(A)
+    n = size(B, 1)
+    n == 0 && return A
+    if size(A) == (n, n)
+        fill!(A, zero(T))
+        @inbounds for i in 1:n - 1
+            A[i,i] = B.dv[i]
+            if B.uplo == 'U'
+                A[i, i + 1] = B.ev[i]
+            else
+                A[i + 1, i] = B.ev[i]
+            end
+        end
+        A[n,n] = B.dv[n]
+        return A
+    else
+        return @invoke copyto!(A::AbstractMatrix, B::AbstractMatrix)
+    end
+end
+
 #Converting from Bidiagonal to Tridiagonal
 function Tridiagonal{T}(A::Bidiagonal) where T
     dv = convert(AbstractVector{T}, A.dv)
diff --git a/stdlib/LinearAlgebra/src/diagonal.jl b/stdlib/LinearAlgebra/src/diagonal.jl
index 4b7d9bd9d4af1..9c0b984ae388a 100644
--- a/stdlib/LinearAlgebra/src/diagonal.jl
+++ b/stdlib/LinearAlgebra/src/diagonal.jl
@@ -91,6 +91,20 @@ similar(D::Diagonal, ::Type{T}) where {T} = Diagonal(similar(D.diag, T))
 similar(::Diagonal, ::Type{T}, dims::Union{Dims{1},Dims{2}}) where {T} = zeros(T, dims...)
 
 copyto!(D1::Diagonal, D2::Diagonal) = (copyto!(D1.diag, D2.diag); D1)
+function copyto!(A::AbstractMatrix{T}, D::Diagonal) where {T}
+    require_one_based_indexing(A)
+    n = length(D.diag)
+    n == 0 && return A
+    if size(A) == (n, n)
+        fill!(A, zero(T))
+        @inbounds for i in 1:n
+            A[i, i] = D.diag[i]
+        end
+        return A
+    else
+        return @invoke copyto!(A::AbstractMatrix, D::AbstractMatrix)
+    end
+end
 
 size(D::Diagonal) = (n = length(D.diag); (n,n))
 
diff --git a/stdlib/LinearAlgebra/src/special.jl b/stdlib/LinearAlgebra/src/special.jl
index ad2c97568c536..d87554127e459 100644
--- a/stdlib/LinearAlgebra/src/special.jl
+++ b/stdlib/LinearAlgebra/src/special.jl
@@ -300,9 +300,9 @@ lmul!(Q::Adjoint{<:Any,<:QRPackedQ}, B::AbstractTriangular) = lmul!(Q, full!(B))
 function _qlmul(Q::AbstractQ, B)
     TQB = promote_type(eltype(Q), eltype(B))
     if size(Q.factors, 1) == size(B, 1)
-        Bnew = Matrix{TQB}(B)
+        Bnew = copy_similar(B, TQB)
     elseif size(Q.factors, 2) == size(B, 1)
-        Bnew = [Matrix{TQB}(B); zeros(TQB, size(Q.factors, 1) - size(B,1), size(B, 2))]
+        Bnew = [copy_similar(B, TQB); zeros(TQB, size(Q.factors, 1) - size(B,1), size(B, 2))]
     else
         throw(DimensionMismatch("first dimension of matrix must have size either $(size(Q.factors, 1)) or $(size(Q.factors, 2))"))
     end
@@ -331,9 +331,9 @@ function _qrmul(A, adjQ::Adjoint{<:Any,<:AbstractQ})
     Q = adjQ.parent
     TAQ = promote_type(eltype(A), eltype(Q))
     if size(A,2) == size(Q.factors, 1)
-        Anew = Matrix{TAQ}(A)
+        Anew = copy_similar(A, TAQ)
     elseif size(A,2) == size(Q.factors,2)
-        Anew = [Matrix{TAQ}(A) zeros(TAQ, size(A, 1), size(Q.factors, 1) - size(Q.factors, 2))]
+        Anew = [copy_similar(A, TAQ) zeros(TAQ, size(A, 1), size(Q.factors, 1) - size(Q.factors, 2))]
     else
         throw(DimensionMismatch("matrix A has dimensions $(size(A)) but matrix B has dimensions $(size(Q))"))
     end
diff --git a/stdlib/LinearAlgebra/src/tridiag.jl b/stdlib/LinearAlgebra/src/tridiag.jl
index 5a3c7612f6784..354bc38424fd7 100644
--- a/stdlib/LinearAlgebra/src/tridiag.jl
+++ b/stdlib/LinearAlgebra/src/tridiag.jl
@@ -122,17 +122,23 @@ SymTridiagonal(S::SymTridiagonal) = S
 AbstractMatrix{T}(S::SymTridiagonal) where {T} =
     SymTridiagonal(convert(AbstractVector{T}, S.dv)::AbstractVector{T},
                    convert(AbstractVector{T}, S.ev)::AbstractVector{T})
-function Matrix{T}(M::SymTridiagonal) where T
+Matrix{T}(M::SymTridiagonal) where {T} = copyto!(Matrix{T}(undef, size(M)), M)
+function copyto!(A::AbstractMatrix{T}, M::SymTridiagonal) where {T}
+    require_one_based_indexing(A)
     n = size(M, 1)
-    Mf = zeros(T, n, n)
-    n == 0 && return Mf
-    @inbounds for i = 1:n-1
-        Mf[i,i] = symmetric(M.dv[i], :U)
-        Mf[i+1,i] = transpose(M.ev[i])
-        Mf[i,i+1] = M.ev[i]
+    n == 0 && return A
+    if size(A) == (n, n)
+        fill!(A, zero(T))
+        @inbounds for i in 1:n-1
+            A[i,i] = symmetric(M.dv[i], :U)
+            A[i+1,i] = transpose(M.ev[i])
+            A[i,i+1] = M.ev[i]
+        end
+        A[n,n] = symmetric(M.dv[n], :U)
+        return A
+    else
+        return @invoke copyto!(A::AbstractMatrix, M::AbstractMatrix)
     end
-    Mf[n,n] = symmetric(M.dv[n], :U)
-    return Mf
 end
 Matrix(M::SymTridiagonal{T}) where {T} = Matrix{T}(M)
 Array(M::SymTridiagonal) = Matrix(M)
@@ -571,16 +577,24 @@ function size(M::Tridiagonal, d::Integer)
     end
 end
 
-function Matrix{T}(M::Tridiagonal{T}) where T
-    A = zeros(T, size(M))
-    for i = 1:length(M.d)
-        A[i,i] = M.d[i]
-    end
-    for i = 1:length(M.d)-1
-        A[i+1,i] = M.dl[i]
-        A[i,i+1] = M.du[i]
+Matrix{T}(M::Tridiagonal) where {T} = copyto!(Matrix{T}(undef, size(M)), M)
+
+function copyto!(A::AbstractMatrix{T}, M::Tridiagonal) where {T}
+    require_one_based_indexing(A)
+    n = size(M, 1)
+    n == 0 && return A
+    if size(A) == (n, n)
+        fill!(A, zero(T))
+        @inbounds for i = 1:n-1
+            A[i,i] = M.d[i]
+            A[i+1,i] = M.dl[i]
+            A[i,i+1] = M.du[i]
+        end
+        A[n,n] = M.d[n]
+        return A
+    else
+        @invoke copyto!(A::AbstractMatrix, M::AbstractMatrix)
     end
-    A
 end
 Matrix(M::Tridiagonal{T}) where {T} = Matrix{T}(M)
 Array(M::Tridiagonal) = Matrix(M)
diff --git a/stdlib/LinearAlgebra/test/special.jl b/stdlib/LinearAlgebra/test/special.jl
index 9b094c267d41b..cfb1795292bf6 100644
--- a/stdlib/LinearAlgebra/test/special.jl
+++ b/stdlib/LinearAlgebra/test/special.jl
@@ -429,12 +429,13 @@ end
     dl = [1, 1, 1]
     d = [1, 1, 1, 1]
     D = Diagonal(d)
-    Bi = Bidiagonal(d, dl, :L)
+    Bl = Bidiagonal(d, dl, :L)
+    Bu = Bidiagonal(d, dl, :U)
     Tri = Tridiagonal(dl, d, dl)
     Sym = SymTridiagonal(d, dl)
     F = qr(ones(4, 1))
     A = F.Q'
-    for A in (F.Q, F.Q'), B in (D, Bi, Tri, Sym)
+    for A in (F.Q, F.Q'), B in (D, Bl, Bu, Tri, Sym)
         @test B*A ≈ Matrix(B)*A
         @test A*B ≈ A*Matrix(B)
     end