## Certain aspects of the theory of equations for a pair of matrices |

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### Contents

BA CONTENTS | 2 |

A Necessary Condition for Property P3 | 5 |

Properties P and Pz for Third Order Matrices | 11 |

7 other sections not shown

### Common terms and phrases

charac characteristic and minimum characteristic equation chosen classic canonical form common invariant direction common right invariant Commutative Matrices Condition for Property Corallary different from zero direction r s distinct characteristic values distinct elementary divisors distinct roots equa equal characteristic values equation of F equation whose roots form of type Geometric Progression Hence invariant direction r s left invariant direction Lemma linear elementary divisors main diagonal minimum equation necessary and sufficient non-singular second order notation Pairing of Characteristic product in pairs Prom property P3 prove Theorem rank of g(D right invariant direction roots of a(x rows satisfies the condition scalar matrix second equation second order matrices Similarly sufficient condition T B T teristic values THEORY OF EQUATIONS Third Order Matrices tic values tion trices values are paired values of F zero matrix