Let $ K $ be a field. We can recursively define matrices as
$ M_{a} = (a)$ for any $ a\in K $ and
$$ M_{a_1, \cdots, a_{2^i}} = (
\begin{matrix}
M_{a_1, \cdots, a_{2^{i-1}}} & M_{a_{2^{i-1} +1}, \cdots, a_{2^i}}\\
M_{a_{2^{i-1} +1}, \cdots, a_{2^i}} & M_{a_1, \cdots, a_{2^{i-1}}}\\
\end{matrix}
) $$$$ M_{a_1, \cdots, a_{2^i}} =
\begin{pmatrix}
M_{a_1, \cdots, a_{2^{i-1}}} & M_{a_{2^{i-1} +1}, \cdots, a_{2^i}}\\
M_{a_{2^{i-1} +1}, \cdots, a_{2^i}} & M_{a_1, \cdots, a_{2^{i-1}}}\\
\end{pmatrix}
$$
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
$$ M_{a_1, a_2, \cdots, a_{2^n}} - Diagonal ( b_1, b_2, \cdots, b_{2^n})? $$$$ M_{a_1, a_2, \cdots, a_{2^n}} - \operatorname{diag} ( b_1, b_2, \cdots, b_{2^n})? $$
