for all .
Examples of reciprocal polynomials are Gaussian polynomials, as well as the characteristic polynomials of orthogonal matrices (including the identity matrix as a special case), symplectic matrices, involution matrices (http://planetmath.org/LinearInvolution), and the Pascal matrices .
It is clear that if is a zero for a reciprocal polynomial, then is also a zero. This property motivates the name. This means that the spectra of matrices of above type is symmetric with respect to the unit circle in ; if is an eigenvalue, so is .
- 1 H. Eves, Elementary Matrix Theory, Dover publications, 1980.
- 2 N.J. Higham, Accuracy and Stability of Numerical Algorithms, 2nd ed., SIAM, 2002.
|Date of creation||2013-03-22 13:36:33|
|Last modified on||2013-03-22 13:36:33|
|Last modified by||rspuzio (6075)|