@MISC{VECTSP11.MIZ,
  AUTHOR = {P\c{a}k, Karol},
  TITLE = {Eigenvalues of a Linear Transformation},
  SECTION1 = {Preliminaries},
  SECTION2 = {Maps with Eigenvalues},
  SECTION3 = {Generalized Eigenspace of a Linear Transformation},
  DAY = {11},
  MONTH = {July},
  YEAR = {2008},
  ADDRESS1 = {University of Bialystok, ul. Akademicka 2, 15-267 Bialystok},
  SUMMARY = {The article presents well known facts about eigenvalues of
       linear transformation of a vector space (see \cite{HerstenWinter}).
       We formalize main dependencies between eigenvalues and the
       diagram of the matrix of a linear transformation
       over a finite-dimensional
       vector space. Finally, we formalize the subspace
       $\displaystyle\bigcup_{i=0}^\infty {\rm Ker}(f-\lambda I)^i$
       called a generalized eigenspace for the eigenvalue $\lambda$ and show
       its basic properties.}}

@BOOK{HerstenWinter,
        AUTHOR = {Herstein, I.N. and Winter, David J.},
         TITLE = {Matrix Theory and Linear Algebra},
     PUBLISHER = {Macmillan},
          YEAR = {1988}}
