Let $ K $ be a field.  We can recursively define  matrices as
$ M_{a} = (a)$ for any $ a\in K $  and
$$ M_{a_1, \cdots, a_{2^i}} = 
\begin{matrix}
  M_{a_1, \cdots, a_{2^{i-1}}} & M_{a_{2^{i-1} +1, \cdots, a_{2^i}}\\
  M_{a_{2^{i-1} +1, \cdots, a_{2^i}} &   M_{a_1, \cdots, a_{2^{i-1}}}
\end{matrix} $$
when $ i>0 $ and $a_j\in K$.  
What is the name for the type of matrices?
Let $ a_1, a_2, \cdots, a_{2^n} $ and
$ b_1, b_2, \cdots, b_{2^n} $ be two list of elements in $ K $.
Is there a formula for the eigenvalues of 
\[  M_{a_1, a_2, \cdots, a_{2^n}} - Diagonal ( b_1, b_2, \cdots, b_{2^n})? \]