Vectors and Matrices |
Contents
CHAPTER PAGE I SYSTEMS OF LINEAR EQUATIONS 1 Graphs 36 | 3 |
Equivalence of systems | 6 |
Elementary operations | 8 |
Copyright | |
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A₁ B₁ B₂ basic vectors called canonical form coefficients in F column vectors common left multiple common right divisor companion matrix COROLLARY D₁ define degree denote determinant 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 integer invariant factors invariant space inverse irreducible isomorphism ith row k₁ linear combination linear system linearly independent matrices with elements minimum function m(x nomials non-derogatory non-singular matrix non-zero null space obtained operation of Type orthogonal complement orthogonal matrix P-¹AP permutation polynomial principal diagonal proved THEOREM relatively prime ring with unit row rank row vectors S₁ scalar singular solution span subspaces symmetric symmetric matrix system of equations tion unique unit element vector space vectors 33 Φι