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I have a matrix which is kind of symmetrical with the other diagonal, i.e., something like

$$A = \left[ \begin{array}{c c c c} a & b & c & d \\ e & f & g & c \\ h & i & f & b \\ j & h & e & a \end{array} \right]$$

Does this matrix have a special name in literature? What are it's properties?

And a matrix that is symmetrical by both diagonals

$$A = \left[ \begin{array}{c c c c} a & b & c & d \\ b & e & f & c \\ c & f & e & b \\ d & c & b & a \end{array} \right]$$

What's the name of it? Any interesting properties?

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    $\begingroup$ The second is bisymmetric. I don't know a name for the more general first. $\endgroup$ – André Nicolas May 1 '13 at 22:10
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    $\begingroup$ The first is a persymmetric matrix. $\endgroup$ – Scott H. May 1 '13 at 22:10
  • $\begingroup$ relevant question on persymmetric matrices $\endgroup$ – Omnomnomnom May 27 '19 at 21:02
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(Turning the comments into an answer)

Yes, the first matrix is persymmetric, and the second is bisymmetric.

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