Pairs of normal matrices with property L
Helmut Wielandt · Journal of research of the National Bureau of Standards · 1953
A short proof is given , under weaker ass ump tions, of t he foll owi ng theore m firs t proverl by K. Wiegman n: If t he e igenvalu es a i, /3i of t wo normal n X n matrices A, B may be nUIllbered in s uch a wa .vthat t he eigen values I' i(Z) of C ( z )= a +zb are given by I'i(Z) = I' i+ Z/3 i (fo r i = J , . . .,n a nd all co m plex values of z) , t hen AB= BA.