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单词 Circulant Determinant
释义

Circulant Determinant

Gradshteyn and Ryzhik (1970) define circulants by


(1)

where is the th Root of Unity. The second-order circulant determinant is
(2)

and the third order is


(3)

where and are the Complex Cube Roots of Unity.


The Eigenvalues of the corresponding circulant matrix are

(4)

See also Circulant Matrix


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.


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