Do you know these matrices described by Alan Rendall? If so, please point out a source where he may find more information about them. I am interested in knowing too!

Hydrobates

I have come across a class of matrices with some interesting properties. I feel that they must be known but I have not been able to find anything written about them. This is probably just because I do not know the right place to look. I will describe these matrices here and I hope that somebody will be able to point out a source where I can find more information about them. Consider an $latex n\times n$ matrix $latex A$ with elements $latex a_{ij}$ having the following properties. The elements with $latex i=j$ (call them $latex b_i$) are negative. The elements with $latex j=i+1\ {\rm mod}\ n$ (call them $latex c_i$) are positive. All other elements are zero. The determinant of a matrix of this type is $latex \prod_i b_i+(-1)^{n+1}\prod_i c_i$. Notice that the two terms in this sum always have opposite signs. A property of these matrices which I…

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