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--- a/cppdraft/linalg/transp/helpers.md
+++ b/cppdraft/linalg/transp/helpers.md
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+[linalg.transp.helpers]
+
+# 29 Numerics library [[numerics]](./#numerics)
+
+## 29.9 Basic linear algebra algorithms [[linalg]](linalg#transp.helpers)
+
+### 29.9.10 Transpose in-place transformation [[linalg.transp]](linalg.transp#helpers)
+
+#### 29.9.10.2 Exposition-only helpers for layout_transpose and transposed [linalg.transp.helpers]
+
+[1](#1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12955)
+
+The exposition-only *transpose-extents* function
+takes an extents object representing the extents of a matrix,
+and returns a new extents object
+representing the extents of the transpose of the matrix[.](#1.sentence-1)
+
+[2](#2)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12961)
+
+The exposition-only alias template*transpose-extents-t*<InputExtents> gives the type of *transpose-extents*(e) for a given extents object e of type InputExtents[.](#2.sentence-1)
+
+[ð](#itemdecl:1)
+
+`template<class IndexType, size_t InputExtent0, size_t InputExtent1>
+  constexpr extents<IndexType, InputExtent1, InputExtent0>
+    transpose-extents(const extents<IndexType, InputExtent0, InputExtent1>& in);   // exposition only
+`
+
+[3](#3)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12973)
+
+*Returns*: extents<IndexType, InputExtent1, InputExtent0>(in.extent(1), in.extent(0))
+
+template<class InputExtents>using *transpose-extents-t* =decltype(*transpose-extents*(declval<InputExtents>())); // *exposition only*
--- a/cppdraft/linalg/transp/intro.md
+++ b/cppdraft/linalg/transp/intro.md
@@ -0,0 +1,23 @@
+[linalg.transp.intro]
+
+# 29 Numerics library [[numerics]](./#numerics)
+
+## 29.9 Basic linear algebra algorithms [[linalg]](linalg#transp.intro)
+
+### 29.9.10 Transpose in-place transformation [[linalg.transp]](linalg.transp#intro)
+
+#### 29.9.10.1 Introduction [linalg.transp.intro]
+
+[1](#1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12943)
+
+layout_transpose is an mdspan layout mapping policy
+that swaps the two indices, extents, and strides
+of any unique mdspan layout mapping policy[.](#1.sentence-1)
+
+[2](#2)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12948)
+
+The transposed function takes an mdspan representing a matrix, and returns a new mdspan representing the transpose of the input matrix[.](#2.sentence-1)
--- a/cppdraft/linalg/transp/layout/transpose.md
+++ b/cppdraft/linalg/transp/layout/transpose.md
@@ -0,0 +1,102 @@
+[linalg.transp.layout.transpose]
+
+# 29 Numerics library [[numerics]](./#numerics)
+
+## 29.9 Basic linear algebra algorithms [[linalg]](linalg#transp.layout.transpose)
+
+### 29.9.10 Transpose in-place transformation [[linalg.transp]](linalg.transp#layout.transpose)
+
+#### 29.9.10.3 Class template layout_transpose [linalg.transp.layout.transpose]
+
+[1](#1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12986)
+
+layout_transpose is an mdspan layout mapping policy
+that swaps the two indices, extents, and strides
+of any mdspan layout mapping policy[.](#1.sentence-1)
+
+namespace std::linalg {template<class Layout>class [layout_transpose](#lib:layout_transpose "29.9.10.3 Class template layout_transpose [linalg.transp.layout.transpose]") {public:using nested_layout_type = Layout; template<class Extents>struct mapping {private:using *nested-mapping-type* =typename Layout::template mapping<*transpose-extents-t*<Extents>>; // *exposition only*public:using extents_type = Extents; using index_type = typename extents_type::index_type; using size_type = typename extents_type::size_type; using rank_type = typename extents_type::rank_type; using layout_type = layout_transpose; constexpr explicit mapping(const *nested-mapping-type*&); constexpr const extents_type& extents() const noexcept { return *extents_*; }constexpr index_type required_span_size() const{ return *nested-mapping_*.required_span_size(); template<class Index0, class Index1>constexpr index_type operator()(Index0 ind0, Index1 ind1) const{ return *nested-mapping_*(ind1, ind0); }constexpr const *nested-mapping-type*& nested_mapping() const noexcept{ return *nested-mapping_*; }static constexpr bool is_always_unique() noexcept{ return *nested-mapping-type*::is_always_unique(); }static constexpr bool is_always_exhaustive() noexcept{ return *nested-mapping-type*::is_always_exhaustive(); }static constexpr bool is_always_strided() noexcept{ return *nested-mapping-type*::is_always_strided(); }constexpr bool is_unique() const { return *nested-mapping_*.is_unique(); }constexpr bool is_exhaustive() const { return *nested-mapping_*.is_exhaustive(); }constexpr bool is_strided() const { return *nested-mapping_*.is_strided(); }constexpr index_type stride(size_t r) const; template<class OtherExtents>friend constexpr bool operator==(const mapping& x, const mapping<OtherExtents>& y); }; private:*nested-mapping-type* *nested-mapping_*; // *exposition only* extents_type *extents_*; // *exposition only*};}
+
+[2](#2)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13049)
+
+Layout shall meet
+the layout mapping policy requirements ([[mdspan.layout.policy.reqmts]](mdspan.layout.policy.reqmts "23.7.3.4.3 Layout mapping policy requirements"))[.](#2.sentence-1)
+
+[3](#3)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13053)
+
+*Mandates*: 
+
+- [(3.1)](#3.1)
+
+Extents is a specialization of std::extents, and
+
+- [(3.2)](#3.2)
+
+Extents::rank() equals 2[.](#3.sentence-1)
+
+[ð](#lib:layout_transpose::mapping,constructor)
+
+`constexpr explicit mapping(const nested-mapping-type& map);
+`
+
+[4](#4)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13068)
+
+*Effects*: 
+
+- [(4.1)](#4.1)
+
+Initializes *nested-mapping_* with map, and
+
+- [(4.2)](#4.2)
+
+initializes *extents_* with *transpose-extents*(map.extents())[.](#4.sentence-1)
+
+[ð](#lib:layout_transpose::mapping,stride)
+
+`constexpr index_type stride(size_t r) const;
+`
+
+[5](#5)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13085)
+
+*Preconditions*: 
+
+- [(5.1)](#5.1)
+
+is_strided() is true, and
+
+- [(5.2)](#5.2)
+
+r < 2 is true[.](#5.sentence-1)
+
+[6](#6)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13094)
+
+*Returns*: *nested-mapping_*.stride(r == 0 ? 1 : 0)
+
+[ð](#lib:layout_transpose::mapping,operator==)
+
+`template<class OtherExtents>
+  friend constexpr bool operator==(const mapping& x, const mapping<OtherExtents>& y);
+`
+
+[7](#7)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13106)
+
+*Constraints*: The expressionx.*nested-mapping_* == y.*nested-mapping_* is well-formed and its result is convertible to bool[.](#7.sentence-1)
+
+[8](#8)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13112)
+
+*Returns*: x.*nested-mapping_* == y.*nested-mapping_*[.](#8.sentence-1)
--- a/cppdraft/linalg/transp/transposed.md
+++ b/cppdraft/linalg/transp/transposed.md
@@ -0,0 +1,135 @@
+[linalg.transp.transposed]
+
+# 29 Numerics library [[numerics]](./#numerics)
+
+## 29.9 Basic linear algebra algorithms [[linalg]](linalg#transp.transposed)
+
+### 29.9.10 Transpose in-place transformation [[linalg.transp]](linalg.transp#transposed)
+
+#### 29.9.10.4 Function template transposed [linalg.transp.transposed]
+
+[1](#1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13119)
+
+The transposed function
+takes a rank-2 mdspan representing a matrix, and
+returns a new mdspan representing the input matrix's transpose[.](#1.sentence-1)
+
+The input matrix's data are not modified, and
+the returned mdspan accesses the input matrix's data in place[.](#1.sentence-2)
+
+[ð](#lib:transposed)
+
+`  template<class ElementType, class Extents, class Layout, class Accessor>
+    constexpr auto transposed(mdspan<ElementType, Extents, Layout, Accessor> a);
+`
+
+[2](#2)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13132)
+
+*Mandates*: Extents::rank() == 2 is true[.](#2.sentence-1)
+
+[3](#3)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13136)
+
+Let ReturnExtents be*transpose-extents-t*<Extents>[.](#3.sentence-1)
+
+Let R bemdspan<ElementType, ReturnExtents, ReturnLayout, Accessor>,
+where ReturnLayout is:
+
+- [(3.1)](#3.1)
+
+layout_right if Layout is layout_left;
+
+- [(3.2)](#3.2)
+
+otherwise, layout_left if Layout is layout_right;
+
+- [(3.3)](#3.3)
+
+otherwise, layout_right_padded<PaddingValue> if Layout is  
+layout_left_padded<PaddingValue> for some size_t value PaddingValue;
+
+- [(3.4)](#3.4)
+
+otherwise, layout_left_padded<PaddingValue> if Layout is  
+layout_right_padded<PaddingValue> for some size_t value PaddingValue;
+
+- [(3.5)](#3.5)
+
+otherwise, layout_stride if Layout is layout_stride;
+
+- [(3.6)](#3.6)
+
+otherwise,layout_blas_packed<OppositeTriangle, OppositeStorageOrder>,
+if Layout is  
+layout_blas_packed<Triangle, StorageOrder> for some Triangle and StorageOrder, where
+  * [(3.6.1)](#3.6.1)
+
+OppositeTriangle isconditional_t<is_same_v<Triangle, upper_triangle_t>,
+ lower_triangle_t, upper_triangle_t> and
+
+  * [(3.6.2)](#3.6.2)
+
+OppositeStorageOrder isconditional_t<is_same_v<StorageOrder, column_major_t>, row_major_t, column_major_t>
+
+- [(3.7)](#3.7)
+
+otherwise, NestedLayout if Layout is layout_transpose<NestedLayout> for some NestedLayout;
+
+- [(3.8)](#3.8)
+
+otherwise, layout_transpose<Layout>[.](#3.sentence-2)
+
+[4](#4)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13185)
+
+*Returns*: With ReturnMapping being
+the type typename ReturnLayout::template mapping<ReturnExtents>:
+
+- [(4.1)](#4.1)
+
+if Layout is layout_left, layout_right, or
+a specialization of layout_blas_packed,R(a.data_handle(), ReturnMapping(*transpose-extents*(a.mapping().extents())),
+ a.accessor())
+
+- [(4.2)](#4.2)
+
+otherwise,R(a.data_handle(), ReturnMapping(*transpose-extents*(a.mapping().extents()),
+ a.mapping().stride(1)), a.accessor()) if Layout is layout_left_padded<PaddingValue> for some size_t value PaddingValue;
+
+- [(4.3)](#4.3)
+
+otherwise,R(a.data_handle(), ReturnMapping(*transpose-extents*(a.mapping().extents()),
+ a.mapping().stride(0)), a.accessor()) if Layout is layout_right_padded<PaddingValue> for some size_t value PaddingValue;
+
+- [(4.4)](#4.4)
+
+otherwise, if Layout is layout_stride,R(a.data_handle(), ReturnMapping(*transpose-extents*(a.mapping().extents()),
+ array{a.mapping().stride(1), a.mapping().stride(0)}), a.accessor())
+
+- [(4.5)](#4.5)
+
+otherwise, if Layout is a specialization of layout_transpose,R(a.data_handle(), a.mapping().nested_mapping(), a.accessor())
+
+- [(4.6)](#4.6)
+
+otherwise,R(a.data_handle(), ReturnMapping(a.mapping()), a.accessor())
+
+[5](#5)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13232)
+
+[*Example [1](#example-1)*: void test_transposed(mdspan<double, extents<size_t, 3, 4>> a) {const auto num_rows = a.extent(0); const auto num_cols = a.extent(1); auto a_t = transposed(a);
+ assert(num_rows == a_t.extent(1));
+ assert(num_cols == a_t.extent(0));
+ assert(a.stride(0) == a_t.stride(1));
+ assert(a.stride(1) == a_t.stride(0)); for (size_t row = 0; row < num_rows; ++row) {for (size_t col = 0; col < num_rows; ++col) { assert(a[row, col] == a_t[col, row]); }}auto a_t_t = transposed(a_t);
+ assert(num_rows == a_t_t.extent(0));
+ assert(num_cols == a_t_t.extent(1));
+ assert(a.stride(0) == a_t_t.stride(0));
+ assert(a.stride(1) == a_t_t.stride(1)); for (size_t row = 0; row < num_rows; ++row) {for (size_t col = 0; col < num_rows; ++col) { assert(a[row, col] == a_t_t[row, col]); }}} â *end example*]