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duality theorem |
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duality theorem [dü′al·əd·ē ‚thir·əm]
(mathematics) A theorem which asserts that for a givenn-dimensional space, the (n-p) dimensional homology group is isomorphic to ap-dimensional cohomology group for eachp= 0, …,n, provided certain conditions are met. LetGbe either a compact group or a discrete group, letXbe its character group, and letG′be the character group ofX; then there is an isomorphism ofGontoG′so that the groupsGandG′may be identified. If either of two dual linear-programming problems has a solution, then so does the other. Want to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit the webmaster's page for free fun content. |
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No references found | Chapters discuss duality, linear mappings, matrices, determinant and trace, spectral theory, Euclidean structure, calculus of vector- and matrix-valued functions, matrix inequalities, kinematics and dynamics, convexity, the duality theorem, normed liner spaces, linear mappings between normed linear spaces, positive matrices, and solutions of systems of linear equations. ]From the paper [4], we have the duality theorem which says that the Laplace transform is a topological isomorphism from [F'. The graduate textbook illustrates how Cohen-Macaulay rings arise naturally, develops the Hartshorne-Lichtenbaum vanishing theorem, applies two classes of rings to polyhedral geometry, explains Grothendieck's duality theorem, and defines D-modules over rings of differential operators. |
duality theorem |
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