transpose

$A^{\mathsf T}$ — rows of $A$ rewritten as columns.

For an $m\times n$ matrix $A$ , the transpose $A^{\mathsf T}$ is the $n\times m$ matrix defined entry-by-entry by $(A^{\mathsf T})_{ij}=A_{ji}$ : row $i$ of $A$ becomes column $i$ of $A^{\mathsf T}$ . Transposing twice returns the original matrix, and $(AB)^{\mathsf T}=B^{\mathsf T}A^{\mathsf T}$ — the order reverses. A matrix equal to its own transpose, $A=A^{\mathsf T}$ , is called symmetric.