diff --git a/stdlib/LinearAlgebra/src/adjtrans.jl b/stdlib/LinearAlgebra/src/adjtrans.jl
index 3c5e3b6568c8c..8145b8b71a5e6 100644
--- a/stdlib/LinearAlgebra/src/adjtrans.jl
+++ b/stdlib/LinearAlgebra/src/adjtrans.jl
@@ -139,8 +139,11 @@ convert(::Type{Adjoint{T,S}}, A::Adjoint) where {T,S} = Adjoint{T,S}(convert(S,
 convert(::Type{Transpose{T,S}}, A::Transpose) where {T,S} = Transpose{T,S}(convert(S, A.parent))
 
 # Strides for transposed strided arrays — but only if the elements are actually stored in memory
-Base.strides(A::Adjoint{<:Real, <:StridedArray}) = reverse(strides(A.parent))
-Base.strides(A::Transpose{<:Any, <:StridedArray}) = reverse(strides(A.parent))
+Base.strides(A::Adjoint{<:Real, <:StridedVector}) = (stride(A.parent, 2), stride(A.parent, 1))
+Base.strides(A::Transpose{<:Any, <:StridedVector}) = (stride(A.parent, 2), stride(A.parent, 1))
+# For matrices it's slightly faster to use reverse and avoid calling stride twice
+Base.strides(A::Adjoint{<:Real, <:StridedMatrix}) = reverse(strides(A.parent))
+Base.strides(A::Transpose{<:Any, <:StridedMatrix}) = reverse(strides(A.parent))
 
 # for vectors, the semantics of the wrapped and unwrapped types differ
 # so attempt to maintain both the parent and wrapper type insofar as possible