Correct terminology for a "matrix of array" or a "matrix of vectors"

Question

What is the correct terminology to name the following matrix, that contains arrays as elements?

I would call it as a matrix of arrays or a matrix of vectors, but I am not sure. Other names?

Just to add some further information:

• $a_{ijk}=f_k(P_i,Q_j)$, i.e. the elements of the matrix $A$ are real numbers that result from $k=1,...,K$ different functions that act on a pair of probability distributions, $P_i$ and $Q_j$.
• $(a_{ijk})_{i\ne j}\ge0$, i.e. non-negative off-diagonal elements
• $a_{iik}=a_{jjk}=0$, i.e. diagonal elements equal to zero
• $a_{ijk}=a_{jik}$, i.e. symmetry between $i$ and $j$ elements, for each $k$-function

Just for information, this is the generating Latex code:

A=(a_{ijk})=
\left| 
\begin{array}{c@{}c@{}c}
  \left|\begin{array}{c}
         0 \\
         0 \\
         0 \\
         \vdots \\
         0 \\
  \end{array}\right|
  &  \left|\begin{array}{c}
         a_{121} \\
         a_{122} \\
         a_{123} \\
         \vdots \\
         a_{12K} \\
  \end{array}\right|  
  &  \left|\begin{array}{c}
         a_{131} \\
         a_{132} \\
         a_{133} \\
         \vdots \\
         a_{13K} \\
  \end{array}\right|\\
  \left|\begin{array}{c}
         a_{211} \\
         a_{212} \\
         a_{213} \\
         \vdots \\
         a_{21K} \\
  \end{array}\right| 
  & 
  \left|\begin{array}{c}
         0 \\
         0 \\
         0 \\
         \vdots \\
         0 \\
  \end{array}\right|
  &  \left|\begin{array}{c}
         a_{231} \\
         a_{232} \\
         a_{233} \\
         \vdots \\
         a_{23K} \\
  \end{array}\right|\\
  \left|\begin{array}{c}
         a_{311} \\
         a_{312} \\
         a_{313} \\
         \vdots \\
         a_{31K} \\
  \end{array}\right|  
  &  \left|\begin{array}{c}
         a_{321} \\
         a_{322} \\
         a_{323} \\
         \vdots \\
         a_{32K} \\
  \end{array}\right|
  & 
  \left|\begin{array}{c}
         0 \\
         0 \\
         0 \\
         \vdots \\
         0 \\
  \end{array}\right|
  \\ 
\end{array}\right|