Home/Algebra/Matrices/Transpose16. MatricesTransposeLevel: intermedioIn 16. MatricesFormulaCopy LaTeX(AT)ij=aji;(AB)T=BTAT(A^T)_{ij}=a_{ji};\quad(AB)^T=B^TA^T(AT)ij=aji;(AB)T=BTATTagsalgebraalgebra formulalinearmatricesDetailSwaps rows and columns.Explore the ideaFound an error? Contact us.Related formulasRelatedOrthogonal matrixQTQ=I⇒Q−1=QTQ^TQ=I\Rightarrow Q^{-1}=Q^TQTQ=I⇒Q−1=QTOpen formulaOpen in sectionRelatedNormal equationsATAx^=ATbA^TA\hat x=A^TbATAx^=ATbOpen formulaOpen in section