When there is a difference between algebraic and geometric multiplicity of eigenvalues mainvectors are used to handle that difference. Mainvectors are defined as the solution(adsbygoogle = window.adsbygoogle || []).push({}); vof the equation: (A-lambda*E)^k*v=0 where k is the multiplicity of the eigenvalue lambda. Now my question is: Why are you using the k-th power of the definition of an eigenvector to search for a mainvector? how do you get from the fact that there is a difference between alge./geom. mult. to that equation? thx for answers

(I apologize for not knowing that many mathematical expressions in english. but I hope you guys understand my problem)

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The definition of mainvectors

**Physics Forums | Science Articles, Homework Help, Discussion**