Circulant Determinant
Gradshteyn and Ryzhik (1970) define circulants by
 | (1) |
is the 
th Root of Unity. The second-order circulant determinant is | (2) |
 | (3) |
and 
are the Complex Cube Roots of Unity.The Eigenvalues 
of the corresponding 
circulant matrix are
 | (4) |
References
Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, pp. 1111-1112, 1979. Vardi, I. Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, p. 114, 1991.
- Euler's 6n+1 Theorem
- Euler's Addition Theorem
- Euler's Circle
- Euler's Conjecture
- Euler's Criterion
- Euler's Displacement Theorem
- Euler's Distribution Theorem
- Euler's Factorization Method
- Euler's Finite Difference Transformation
- Euler's Graeco-Roman Squares Conjecture
- Euler's Homogeneous Function Theorem
- Euler's Hypergeometric Transformations
- Euler's Idoneal Number
- Euler's Machin-Like Formula
- Euler's Pentagonal Number Theorem
- Euler's Phi Function
- Euler's Polygon Division Problem
- Euler's Quadratic Residue Theorem
- Euler Square
- Euler's Rotation Theorem
- Euler's Rule
- Euler's Series Transformation
- Euler's Spiral
- Euler's Sum of Powers Conjecture
- Euler's Theorem