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Reference.org
Transpose of a linear map
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<p>In <a href="/facts/Linear_algebra/8VaB4VWk">linear algebra</a>, the transpose of a <a href="/facts/Linear_map/Q1PBKNVV">linear map</a> between two vector spaces, defined over the same <a href="/facts/Field_(mathematics)/xAjAS4ko">field</a>, is an induced map between the <a href="/facts/Dual_space/4Uw4Knz1">dual spaces</a> of the two vector spaces. The transpose or algebraic adjoint of a linear map is often used to study the original linear map. This concept is generalised by <a href="/facts/Adjoint_functors/bJ1P7AN2">adjoint functors</a>. </p>