Definition:Transpose of Matrix

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

Then the transpose of $$\mathbf{A}$$ is denoted $$\mathbf{A}^t$$ and is defined as:

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