Transpose of stacked matrix

Dependencies:

  1. Stacking

Let $A_{i, j}$ be an $m_i$ by $n_j$ matrix.

\[ \begin{bmatrix} A_{1, 1} & A_{1, 2} & \cdots & A_{1, q} \\ A_{2, 1} & A_{2, 2} & \cdots & A_{2, q} \\ \vdots & \vdots & \ddots & \vdots \\ A_{p, 1} & A_{p, 2} & \cdots & A_{p, q} \end{bmatrix}^T = \begin{bmatrix} A_{1, 1}^T & A_{2, 1}^T & \cdots & A_{p, 1}^T \\ A_{1, 2}^T & A_{2, 2}^T & \cdots & A_{p, 2}^T \\ \vdots & \vdots & \ddots & \vdots \\ A_{1, q}^T & A_{2, q}^T & \cdots & A_{p, q}^T \end{bmatrix} \]

Dependency for:

  1. Orthogonal matrix

Info:

Transitive dependencies:

  1. Group
  2. Ring
  3. Semiring
  4. Matrix
  5. Stacking