diff --git a/src/implementations/polar.jl b/src/implementations/polar.jl
index 00f9cbbd..8d224503 100644
--- a/src/implementations/polar.jl
+++ b/src/implementations/polar.jl
@@ -123,6 +123,7 @@ function _left_polarnewton!(A::AbstractMatrix, W, P = similar(A, (0, 0)); tol =
         Rc .= R
         Rᴴinv = ldiv!(UpperTriangular(Rc)', one!(Rᴴinv))
     else # m == n
+        Q = nothing
         R = A
         Rc = view(W, 1:n, 1:n)
         Rc .= R
@@ -163,6 +164,7 @@ function _right_polarnewton!(A::AbstractMatrix, Wᴴ, P = similar(A, (0, 0)); to
         copy!(Lc, L)
         Lᴴinv = ldiv!(LowerTriangular(Lc)', one!(Lᴴinv))
     else # m == n
+        Q = nothing
         L = A
         Lc = view(Wᴴ, 1:m, 1:m)
         Lc .= L
diff --git a/src/implementations/qr.jl b/src/implementations/qr.jl
index f78d8c44..6b1cc58b 100644
--- a/src/implementations/qr.jl
+++ b/src/implementations/qr.jl
@@ -141,6 +141,8 @@ function householder_qr!(
     (inplaceQ && (computeR || positive || blocksize > 1 || m < n)) &&
         throw(ArgumentError("inplace Q only supported if matrix is tall (`m >= n`), R is not required, and using the unblocked algorithm (`blocksize = 1`) with `positive = false`"))
 
+    jpvt = Vector{Int}(undef, 0)
+    τ = Vector{eltype(A)}(undef, 0)
     # Compute QR in packed form
     if blocksize > 1
         nb = min(minmn, blocksize)
diff --git a/src/pullbacks/eig.jl b/src/pullbacks/eig.jl
index a03eb3c4..0cb90cb8 100644
--- a/src/pullbacks/eig.jl
+++ b/src/pullbacks/eig.jl
@@ -135,15 +135,12 @@ function eig_trunc_pullback!(
     (n, n) == size(ΔA) || throw(DimensionMismatch())
     G = V' * V
 
+    VᴴΔV = !iszerotangent(ΔV) ? V' * ΔV : zero(G)
+    ΔVperp = ΔV - V * inv(G) * VᴴΔV
     if !iszerotangent(ΔV)
         (n, p) == size(ΔV) || throw(DimensionMismatch())
-        VᴴΔV = V' * ΔV
         check_eig_cotangents(D, VᴴΔV; degeneracy_atol, gauge_atol)
-
-        ΔVperp = ΔV - V * inv(G) * VᴴΔV
         VᴴΔV .*= conj.(inv_safe.(transpose(D) .- D, degeneracy_atol))
-    else
-        VᴴΔV = zero(G)
     end
 
     if !iszerotangent(ΔDmat)
diff --git a/src/pullbacks/svd.jl b/src/pullbacks/svd.jl
index 01fdc4f7..fe20608b 100644
--- a/src/pullbacks/svd.jl
+++ b/src/pullbacks/svd.jl
@@ -47,6 +47,8 @@ function svd_pullback!(
     Ur = view(U, :, 1:r)
     Vᴴr = view(Vᴴ, 1:r, :)
     Sr = view(S, 1:r)
+    indU = axes(U, 2)
+    indV = axes(Vᴴ, 1)
 
     # Extract and check the cotangents
     ΔU, ΔSmat, ΔVᴴ = ΔUSVᴴ
diff --git a/src/yalapack.jl b/src/yalapack.jl
index 576fe3c5..78dd81a8 100644
--- a/src/yalapack.jl
+++ b/src/yalapack.jl
@@ -2033,6 +2033,7 @@ for (gesvd, gesdd, gesvdx, gejsv, gesvj, elty, relty) in
             for i in 1:2  # first call returns lwork as work[1]
                 #! format: off
                 if eltype(A) <: Complex
+                    rwork_ = isnothing(rwork) ? Vector{$relty}(undef, 0) : rwork
                     ccall((@blasfunc($gesvd), libblastrampoline), Cvoid,
                           (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                            Ptr{$relty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
@@ -2040,7 +2041,7 @@ for (gesvd, gesdd, gesvdx, gejsv, gesvj, elty, relty) in
                            Ptr{BlasInt}, Clong, Clong),
                           jobu, jobvt, m, n, A, lda,
                           S, U, ldu, Vᴴ, ldv,
-                          work, lwork, rwork,
+                          work, lwork, rwork_,
                           info, 1, 1)
                 else
                     ccall((@blasfunc($gesvd), libblastrampoline), Cvoid,
@@ -2135,6 +2136,7 @@ for (gesvd, gesdd, gesvdx, gejsv, gesvj, elty, relty) in
             for i in 1:2  # first call returns lwork as work[1]
                 #! format: off
                 if eltype(A) <: Complex
+                    rwork_ = isnothing(rwork) ? Vector{$relty}(undef, 0) : rwork
                     ccall((@blasfunc($gesdd), libblastrampoline), Cvoid,
                           (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                            Ptr{$relty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
@@ -2142,7 +2144,7 @@ for (gesvd, gesdd, gesvdx, gejsv, gesvj, elty, relty) in
                            Ptr{BlasInt}, Clong),
                           job, m, n, A, lda,
                           S, U, ldu, Vᴴ, ldv,
-                          work, lwork, rwork, iwork,
+                          work, lwork, rwork_, iwork,
                           info, 1)
                 else
                     ccall((@blasfunc($gesdd), libblastrampoline), Cvoid,