diff --git a/base/linalg/rowvector.jl b/base/linalg/rowvector.jl
index e38111fd7e1d79..510de6004bc8f8 100644
--- a/base/linalg/rowvector.jl
+++ b/base/linalg/rowvector.jl
@@ -114,32 +114,13 @@ julia> conj(v)
 IndexStyle(::RowVector) = IndexLinear()
 IndexStyle(::Type{<:RowVector}) = IndexLinear()
 
-@propagate_inbounds getindex(rowvec::RowVector, i) = transpose(rowvec.vec[i])
-@propagate_inbounds setindex!(rowvec::RowVector, v, i) = setindex!(rowvec.vec, transpose(v), i)
-
-# Cartesian indexing is distorted by getindex
-# Furthermore, Cartesian indexes don't have to match shape, apparently!
-@inline function getindex(rowvec::RowVector, i::CartesianIndex)
-    @boundscheck if !(i.I[1] == 1 && i.I[2] ∈ indices(rowvec.vec)[1] && check_tail_indices(i.I...))
-        throw(BoundsError(rowvec, i.I))
-    end
-    @inbounds return transpose(rowvec.vec[i.I[2]])
-end
-@inline function setindex!(rowvec::RowVector, v, i::CartesianIndex)
-    @boundscheck if !(i.I[1] == 1 && i.I[2] ∈ indices(rowvec.vec)[1] && check_tail_indices(i.I...))
-        throw(BoundsError(rowvec, i.I))
-    end
-    @inbounds rowvec.vec[i.I[2]] = transpose(v)
-end
-
-@propagate_inbounds getindex(rowvec::RowVector, ::CartesianIndex{0}) = getindex(rowvec)
-@propagate_inbounds getindex(rowvec::RowVector, i::CartesianIndex{1}) = getindex(rowvec, i.I[1])
-
-@propagate_inbounds setindex!(rowvec::RowVector, v, ::CartesianIndex{0}) = setindex!(rowvec, v)
-@propagate_inbounds setindex!(rowvec::RowVector, v, i::CartesianIndex{1}) = setindex!(rowvec, v, i.I[1])
+@propagate_inbounds getindex(rowvec::RowVector, i::Int) = transpose(rowvec.vec[i])
+@propagate_inbounds setindex!(rowvec::RowVector, v, i::Int) = setindex!(rowvec.vec, transpose(v), i)
 
-@inline check_tail_indices(i1, i2) = true
-@inline check_tail_indices(i1, i2, i3, is...) = i3 == 1 ? check_tail_indices(i1, i2, is...) : false
+# Keep a RowVector where appropriate
+@propagate_inbounds getindex(rowvec::RowVector, ::Colon, i::Int) = transpose.(rowvec.vec[i:i])
+@propagate_inbounds getindex(rowvec::RowVector, ::Colon, inds::AbstractArray{Int}) = RowVector(rowvec.vec[inds])
+@propagate_inbounds getindex(rowvec::RowVector, ::Colon, ::Colon) = RowVector(rowvec.vec[:])
 
 # helper function for below
 @inline to_vec(rowvec::RowVector) = map(transpose, transpose(rowvec))
diff --git a/test/linalg/diagonal.jl b/test/linalg/diagonal.jl
index 562070e6d7d35f..bb3473d607fe68 100644
--- a/test/linalg/diagonal.jl
+++ b/test/linalg/diagonal.jl
@@ -368,3 +368,7 @@ end
         end
     end
 end
+
+@testset "Diagonal of a RowVector (#23649)" begin
+    @test Diagonal([1,2,3].') == Diagonal([1 2 3])
+end
diff --git a/test/linalg/rowvector.jl b/test/linalg/rowvector.jl
index e63bae94a35b63..f7a1c43312a5d7 100644
--- a/test/linalg/rowvector.jl
+++ b/test/linalg/rowvector.jl
@@ -268,3 +268,23 @@ end
 @testset "ambiguity between * methods with RowVectors and ConjRowVectors (#20971)" begin
     @test RowVector(ConjArray(ones(4))) * ones(4) == 4
 end
+
+@testset "setindex!/getindex" begin
+    v = [2, 3, 4]
+    rv = v.'
+    @test_throws BoundsError setindex!(rv, 5, CartesianIndex((5, 4, 3)))
+    rv[CartesianIndex((1, 1, 1))] = 5
+    @test_throws BoundsError getindex(rv, CartesianIndex((5, 4, 3)))
+    @test rv[1] == 5
+
+    @test rv[:, 2]::Vector == [v[2]]
+    @test rv[:, 2:3]::RowVector == v[2:3].'
+    @test rv[:, :]::RowVector == rv
+
+    v = [1]
+    rv = v.'
+    rv[CartesianIndex()] = 2
+    @test rv[CartesianIndex()] == 2
+    rv[CartesianIndex(1)] = 1
+    @test rv[CartesianIndex(1)] == 1
+end