[linalg.conjtransposed]

# 29 Numerics library [[numerics]](./#numerics)

## 29.9 Basic linear algebra algorithms [[linalg]](linalg#conjtransposed)

### 29.9.11 Conjugate transpose in-place transform [linalg.conjtransposed]

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13268)

The conjugate_transposed function
returns a conjugate transpose view of an object[.](#1.sentence-1)

This combines the effects of transposed and conjugated[.](#1.sentence-2)

[🔗](#lib:conjugate_transposed)

`  template<class ElementType, class Extents, class Layout, class Accessor>
    constexpr auto conjugate_transposed(mdspan<ElementType, Extents, Layout, Accessor> a);
`

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13279)

*Effects*: Equivalent to: return conjugated(transposed(a));

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13284)

[*Example [1](#example-1)*: void test_conjugate_transposed(mdspan<complex<double>, extents<size_t, 3, 4>> a) {const auto num_rows = a.extent(0); const auto num_cols = a.extent(1); auto a_ct = conjugate_transposed(a);
 assert(num_rows == a_ct.extent(1));
 assert(num_cols == a_ct.extent(0));
 assert(a.stride(0) == a_ct.stride(1));
 assert(a.stride(1) == a_ct.stride(0)); for (size_t row = 0; row < num_rows; ++row) {for (size_t col = 0; col < num_rows; ++col) { assert(a[row, col] == conj(a_ct[col, row])); }}auto a_ct_ct = conjugate_transposed(a_ct);
 assert(num_rows == a_ct_ct.extent(0));
 assert(num_cols == a_ct_ct.extent(1));
 assert(a.stride(0) == a_ct_ct.stride(0));
 assert(a.stride(1) == a_ct_ct.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_ct_ct[row, col]);
 assert(conj(a_ct[col, row]) == a_ct_ct[row, col]); }}} — *end example*]