Category:Transposes of Matrices

This category contains results about Transposes of Matrices.
Definitions specific to this category can be found in Definitions/Transposes of Matrices.

Let $\mathbf A = \sqbrk \alpha_{m n}$ be an $m \times n$ matrix over a set.

Then the transpose of $\mathbf A$ is denoted $\mathbf A^\intercal$ and is defined as:

$\mathbf A^\intercal = \sqbrk \beta_{n m}: \forall i \in \closedint 1 n, j \in \closedint 1 m: \beta_{i j} = \alpha_{j i}$