# Is there necessary and sufficient condition on whether a symmetric circulant matrix is non-singular?

Is there necessary and sufficient condition on whether a symmetric circulant matrix is non-singular? I found many example supporting that positive symmetric circulant matrices which has at least two different entries are non-singular.

• Clearly$$\pmatrix{a&b&a&b\cr b&a&b&a\cr a&b&a&b\cr b&a&b&a\cr}$$is singular. – David Dec 15 '14 at 5:45