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I have a problem in transforming a matrix into a block diagonal matrix.

My matrix has the form:

Mat= \begin{array}{cccc} a & b & c & 0 \\ b & 0 & 0 & c \\ c & 0 & 0 & b \\ 0 & c & b & a \\ \end{array}

I want to construct a block diagonal matrix by using Kronecker product and the other process related to matrices.

BDMat=\begin{array}{cc} A & 0 \\ 0 & B \\ \end{array}

where $A$ and $B$ are the 2*2 matrices.

Of course I am looking for a unitary matrix that can create this kind of Block diagonal matrix like U in

U.Mat.Inverse[U]=BDMat
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    $\begingroup$ I don't see how the 4x4 matrix in the beginning and the 2 x 2 block matrix afterwards are related. Would you plese elaborate? $\endgroup$ – Henrik Schumacher Nov 5 '18 at 8:05
  • $\begingroup$ "Of course I am looking for..." You are joking, right? $\endgroup$ – Henrik Schumacher Nov 5 '18 at 11:54
  • $\begingroup$ in second matrix A and B are 2 x 2 and zero is 2 x 2 zero matrix too $\endgroup$ – some Nov 6 '18 at 6:43

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