Matrices / Complex Numbers /eigenvalues+vectors
I really need some help answering this question, it's doing my head in!!
a) let z in the set of C (complex numbers). show that if z+zbar = 0, then Re(z) = 0 (something to do with Argand diagrams?)
(where zbar is z with a horizontal line across the top :S)
b) let A in the set of R^nxn (a square matrix, n by n) be skew-symmetric, that is Atransposed = -A. show that all eigenvalues of A have zero real-part.
c) suppose that x and y are eigenvectors corresponding to distinct eigenvalues of a real-values skew-symmetric matrix. show that (xbartransposed)y=0
can anyone help me solve this please?