Reduction of Matrices to Canonical Form Under Generalized Lorentzian Transformations |
Common terms and phrases
appropriate assume basis calculations canonical form center block CHAPTER characteristic polynomial characteristic roots characteristic vectors choose columns complex consider Corollary corresponding define definition denote determinant diag diagonal blocks elementary divisors equations equivalently exists a standard expression factor final follows form a standard gives hence imply integer J-Lorentzian J-skew matrix J-symmetric matrix J-value Lemma minimum polynomial negative nilpotent non-zero obtain obtain a vector occur orthogonal orthogonal matrix pairwise J-orthogonal positive principal diagonal Professor proof of Theorem prove pure imaginary rank real vectors reduction relation satisfying secondary selection set of real shown similar skew space standard set Suppose symmetric Theorem 13 transformations University V₁ V₂ vectors of index yields zeros elsewhere μ χ