Name for matrix: orthogonal indeed!
in [Math]
|
Prev: Another exact simplification challenge
Next: For n>4 exists a primitive pentanomial of degree n with coef. in Z2
From: JEMebius on 28 Jul 2010 18:34 carlos(a)colorado.edu wrote: > I have a real matrix T, not necessarily orthogonal, > all of whose eigenvalues lie on the unit circle. > Is there a name for it? ("unitary" doesnt fit). The truly complex eigenvalues on the complex unit circle come necessarily in conjugate pairs: otherwise the matrix is not a real one (*). Only +1 and -1 can be single eigenvalues. And then one has a real orthogonal matrix at hand. Ciao: Johan E. Mebius (*) ----------------------------------------------------------------------------------------- Only one counterexample is needed. (A) Consider a 2x2 diagonal matrix with complex conjugate unit eigenvalues. Transform it into a 2D rotation matrix and a 2D reflection matrix by complex similarity transformations. (B) Then find out what happens to a general 2x2 diagonal matrix with unit complex eigenvalues when one applies this similarity transformation. |