diff --git a/stdlib/LinearAlgebra/src/diagonal.jl b/stdlib/LinearAlgebra/src/diagonal.jl
index 8d6f60c3d42f4..5c32058a4b6e9 100644
--- a/stdlib/LinearAlgebra/src/diagonal.jl
+++ b/stdlib/LinearAlgebra/src/diagonal.jl
@@ -405,9 +405,9 @@ end
     end
     out
 end
-_has_matching_storage(out::UpperOrUnitUpperTriangular, A::UpperOrUnitUpperTriangular) = true
-_has_matching_storage(out::LowerOrUnitLowerTriangular, A::LowerOrUnitLowerTriangular) = true
-_has_matching_storage(out, A) = false
+_has_matching_zeros(out::UpperOrUnitUpperTriangular, A::UpperOrUnitUpperTriangular) = true
+_has_matching_zeros(out::LowerOrUnitLowerTriangular, A::LowerOrUnitLowerTriangular) = true
+_has_matching_zeros(out, A) = false
 function _rowrange_tri_stored(B::UpperOrUnitUpperTriangular, col)
     isunit = B isa UnitUpperTriangular
     1:min(col-isunit, size(B,1))
@@ -416,31 +416,27 @@ function _rowrange_tri_stored(B::LowerOrUnitLowerTriangular, col)
     isunit = B isa UnitLowerTriangular
     col+isunit:size(B,1)
 end
-_rowrange_tri_nonstored(B::UpperOrUnitUpperTriangular, col) = col+1:size(B,1)
-_rowrange_tri_nonstored(B::LowerOrUnitLowerTriangular, col) = 1:col-1
+_rowrange_tri_zeros(B::UpperOrUnitUpperTriangular, col) = col+1:size(B,1)
+_rowrange_tri_zeros(B::LowerOrUnitLowerTriangular, col) = 1:col-1
 function __muldiag_nonzeroalpha!(out, D::Diagonal, B::UpperOrLowerTriangular, _add::MulAddMul)
     isunit = B isa UnitUpperOrUnitLowerTriangular
-    out_maybeparent, B_maybeparent = _has_matching_storage(out, B) ? (parent(out), parent(B)) : (out, B)
+    out_maybeparent, B_maybeparent = _has_matching_zeros(out, B) ? (parent(out), parent(B)) : (out, B)
     for j in axes(B, 2)
         # store the diagonal separately for unit triangular matrices
         if isunit
             @inbounds _modify!(_add, D.diag[j] * B[j,j], out, (j,j))
         end
-        # indices of out corresponding to the stored indices of B
+        # The indices of out corresponding to the stored indices of B
         rowrange = _rowrange_tri_stored(B, j)
         @inbounds @simd for i in rowrange
             _modify!(_add, D.diag[i] * B_maybeparent[i,j], out_maybeparent, (i,j))
         end
-        # indices of out corresponding to the zeros of B
+        # Fill the indices of out corresponding to the zeros of B
         # we only fill these if out and B don't have matching zeros
-        if !_has_matching_storage(out, B)
-            rowrange = _rowrange_tri_nonstored(B, j)
-            if haszero(eltype(out))
-                _rmul_or_fill!(@view(out[rowrange,j]), _add.beta)
-            else
-                @inbounds @simd for i in rowrange
-                    _modify!(_add, D.diag[i] * B[i,j], out, (i,j))
-                end
+        if !_has_matching_zeros(out, B)
+            rowrange = _rowrange_tri_zeros(B, j)
+            @inbounds @simd for i in rowrange
+                _modify!(_add, D.diag[i] * B[i,j], out, (i,j))
             end
         end
     end
@@ -476,7 +472,7 @@ function __muldiag_nonzeroalpha!(out, A::UpperOrLowerTriangular, D::Diagonal, _a
     _add_aisone = MulAddMul{true,bis0,Bool,typeof(beta)}(true, beta)
     # if both A and out have the same upper/lower triangular structure,
     # we may directly read and write from the parents
-     out_maybeparent, A_maybeparent = _has_matching_storage(out, A) ? (parent(out), parent(A)) : (out, A)
+     out_maybeparent, A_maybeparent = _has_matching_zeros(out, A) ? (parent(out), parent(A)) : (out, A)
     for j in axes(A, 2)
         dja = _add(@inbounds D.diag[j])
         # store the diagonal separately for unit triangular matrices
@@ -488,16 +484,12 @@ function __muldiag_nonzeroalpha!(out, A::UpperOrLowerTriangular, D::Diagonal, _a
         @inbounds @simd for i in rowrange
             _modify!(_add_aisone, A_maybeparent[i,j] * dja, out_maybeparent, (i,j))
         end
-        # indices of out corresponding to the zeros of A
+        # Fill the indices of out corresponding to the zeros of A
         # we only fill these if out and A don't have matching zeros
-        if !_has_matching_storage(out, A)
-            rowrange = _rowrange_tri_nonstored(A, j)
-            if haszero(eltype(out))
-                _rmul_or_fill!(@view(out[rowrange,j]), _add.beta)
-            else
-                @inbounds @simd for i in rowrange
-                    _modify!(_add, A[i,j] * dja, out, (i,j))
-                end
+        if !_has_matching_zeros(out, A)
+            rowrange = _rowrange_tri_zeros(A, j)
+            @inbounds @simd for i in rowrange
+                _modify!(_add, A[i,j] * dja, out, (i,j))
             end
         end
     end