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acteristic basis ary divisors automorph besis C₁ C₂ canonical basis canonical form chain connecting choose classical canonical form commutes complex components congruent conjugate coordinate system correspondence determine the elementary direct product direct sum divisors of AA equation exists followed G₂ gives greatest common divisor IIIb imaginary and non-singular induction isotropic space L₂ last column last row lemma linearly independent Lorentz Matrices Lorentz transformation MacDuffee Math matrix obtained matrix of order natural order necessary and sufficient non-singular symmetric matrix non-singular transformation P₁ P₂ polynomial proof quadric cone rational canonical form row and last Salp set of elementary set of vectors signature of G single elementary divisor skew matrices solution spinor sufficient condition Suppose symmetric characteristic basis Turnbull and Aitken vino visors zero