Certain Aspects of the Theory of Equations for a Pair of Matrices |
Contents
Introduction | 2 |
Properties P and P₂ for Second Order Matrices | 25 |
Property P3 for Second Order Matrices | 32 |
3 other sections not shown
Common terms and phrases
a₁ a₂ associated B₁ b₁₂ b₂ b₂z c₁ c₂ charac characteristic equation classic canonical form common invariant direction Commutative Matrices Corallary d₁ d₂ direction r s distinct characteristic values distinct elementary divisors distinct roots equa equal characteristic values equation of F example form of type Geometric Progression invariant direction r s k₁ k₁₂ k₂ left invariant direction Lemma linear elementary divisors main diagonal minimum equation necessary and sufficient non-singular matrices non-singular second order notation p₁ P₂ Pairing of Characteristic property P3 R₁ R₂ rank of g(D right invariant direction rows S₂ scalar second equation second order matrices Section square matrix ß₁ ß₂ ẞn sufficient condition teristic values THEORY OF EQUATIONS Third Order Matrices tic values tion transform U₂ V₂ values of F x₁ Y₂ zero matrix α₁ α₂ αι оо ооо