Definition:Transpose of Matrix

Definition
Let $\mathbf A = \left[{\alpha}\right]_{m n}$ be an $m \times n$ matrix.

Then the transpose of $\mathbf A$ is denoted $\mathbf A^t$ (or $\mathbf A^T$) and is defined as:


 * $\mathbf A^t = \left[{\beta}\right]_{n m}: \forall i \in \left[{1 \,.\,.\, n}\right], j \in \left[{1 \,.\,.\, m}\right]: \beta_{i j} = \alpha_{j i}$