Arrangements of HyperplanesSpringer-Verlag, 1992 - 325页 |
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第218页
... matrix of Hess ( f ) with respect to the pair of bases { D ; } and { dx } . It is the usual Hessian matrix of second partial derivatives of f . Lemma 6.8 If g EG , let [ g ] denote the matrix for g in the basis { e } of V so [ g ] i , j ...
... matrix of Hess ( f ) with respect to the pair of bases { D ; } and { dx } . It is the usual Hessian matrix of second partial derivatives of f . Lemma 6.8 If g EG , let [ g ] denote the matrix for g in the basis { e } of V so [ g ] i , j ...
第234页
... matrix of the map . If we choose the basis given in Theorem 6.49 for NG , then the resulting matrix equation connects the Jacobian matrix with the coefficient matrix of the basic derivations and the Hessian matrix . If a1 , ... , a are ...
... matrix of the map . If we choose the basis given in Theorem 6.49 for NG , then the resulting matrix equation connects the Jacobian matrix with the coefficient matrix of the basic derivations and the Hessian matrix . If a1 , ... , a are ...
第289页
... matrix U ( G ) is outlined in Section 6.4 . In a complete matrix U ( G ) , the rows index the types T of the orbits . We use the symbol Ao for the trivial group , the symbols in [ 38 , p.193 ] for irreducible Coxeter groups , G ( r , p ...
... matrix U ( G ) is outlined in Section 6.4 . In a complete matrix U ( G ) , the rows index the types T of the orbits . We use the symbol Ao for the trivial group , the symbols in [ 38 , p.193 ] for irreducible Coxeter groups , G ( r , p ...
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A₁ affine arrangement algebra A(A arrangement and let arrangements of hyperplanes assume b₁ basic invariants basis for D(A braid arrangement Brieskorn broken circuit central arrangement chain complex cohomology complement complex reflection groups complexification compute construction Corollary Coxeter group defining polynomial Definition deformation retraction denote dependent exact sequence Example exterior algebra fiber finite follows from Lemma follows from Proposition formula free arrangement free with exp graded K-module graph H₁ H₂ homogeneous homology homotopy type hyperplane arrangement hyperplanes inductively free integers irreducible isomorphism K-algebra ker(x l-arrangement lattice Lemma Let G linear linearly independent Math matrix maximal element Möbius function modular elements module nonempty Note Orbits Poincaré polynomial poset Proof prove real arrangement Recall reflection arrangement restriction result Section Shephard groups simplicial space subset subspace supersolvable supersolvable arrangement Suppose surjective topological vertex vertices w₁ write x-independent