Reduction of Matrices to Canonical Form Under Generalized Lorentzian Transformations |
Common terms and phrases
a+ib A₁ A²K Ax 2k canonical blocks canonical form center block characteristic polynomial characteristic vector corresponding define diag diagonal blocks direct sum DOCTOR OF PHILOSOPHY elementary divisors exists a standard exists a vector form a standard hence imaginary characteristic root imply index 4k invariant subspace iy(j iµ I)k J-isotropic subspace J-Lorentzian matrix J-orthogonal complement J-orthonormal basis J-skew matrix J-symmetric and J-skew J-symmetric matrix Lemma MacDuffee MATRICES TO CANONICAL minimum polynomial nilpotent J-skew matrices non-singular matrix obtain a vector odd order orthogonal matrix permutation matrix principal diagonal proof of Theorem pure imaginary characteristic real characteristic root real vectors reduction of J-symmetric secondary diagonal set of index set of real standard set symmetric and skew t₁ Theorem 13 V₁ V₂ V2k+j vector in N((A vector v(0 vectors of index Vk+1 Y₂ zeros elsewhere μ χ μν