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CHAPTER PAGE I Systems of Linear Equations 1 Graphs
Equivalence of systems
57 other sections not shown
basic vectors called canonical form characteristic roots column vectors common left multiple common right divisor companion matrix Corollary corresponding define degree denote diagonal element direct sum divisor of zero elementary divisors elementary matrices elementary operation elementary transformation elements in F endomorphism equal equivalent exists a non-singular field F greatest common divisor Hence Hermite form inner product integer invariant factors invariant space isomorphism ith row leading coefficient linear combination linear system linearly independent matrices with elements ment mi(x minimum func minimum function m(x nomials non-derogatory non-singular matrix non-zero null space obtained operation of Type orthogonal complement orthogonal matrix P~iAP permutation poly polynomial principal diagonal proper divisor proved Theorem relatively prime ring with unit row rank row vectors scalar similar singular solution span subspaces symmetric matrix system of equations tion type 35 unique unit element vector space vectors 33 Weyr characteristic