Best Answer

dual space W* of W can naturally identified with linear functionals

Q: Example of linear functional in dual space?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

the significance of duality theory of linear programming

For every polyhedron, there is a dual which is a polyhedron that has:a face where the first had a vertex,a vertex where the first had a face,the same number of edges.A self-dual polyhedron is a polyhedron whose dual is the same shape.All pyramids, for example, are self-dual.

The difference between primal and dual are that primal means an essential, or fundamental of an aspect where as dual means consisting of two parts or elements. Primal is one, dual is two.

There is a dual for every Boolean operation. For example the dual of (a AND b) is not(not A or not B). The first says TRUE if a and b are both TRUE. The second says that FALSE if a is FALSE or b is FALSE. Both statements are equivalent. This equivalency is also referred to by DeMorgan's Theorem.

A dual is almost like the opposite of a given polytope. For example, a regular octahedron is the dual of a cube.Look at the similarities between duals with the example of a cube and regular octahedron:Cube:Vertices: 8Edges: 12Faces: 6Edges per vertex: 3Type of face: square (4-sided)Regular Octahedron:Vertices: 6Edges: 12Faces: 8Edges per vertex: 4Type of face: triangle (3-sided)Both of these shapes can be put together to form a compound and can be rectified to form the same new shape: a cuboctahedron.Also, duals can fit perfectly inside another where each edge touches the face of the other.In this same way a regular dodecahedron is the dual of a regular icosahedron. Some polyhedra like the regular tetrahedron is the dual of itself. All polyhedra have duals. Polygons, polychora, and other polytopes can also have duals in a similar fashion.

Related questions

the significance of duality theory of linear programming

The first dual mission in space started in 1963, space craft: Vostock 5-6 sent by the USSR

The four models of federalism are command federalism, dual federalism, functional federalism and cooperative federalism. The United States uses the dual federalism model.

DUAL table

What are the examples of dual sports

A dual layer DVD has more space compared to a single layer DVD. Instead of holding 4.7GB, a dual layer DVD can hold over 8GB. Aside from more space, they also tend to read faster than single layer ones.

For every polyhedron, there is a dual which is a polyhedron that has:a face where the first had a vertex,a vertex where the first had a face,the same number of edges.A self-dual polyhedron is a polyhedron whose dual is the same shape.All pyramids, for example, are self-dual.

military (national defense)

most likely Chess or checkers

fully understanding the shadow-price interpretation of the optimal simplex multipliers can prove very useful in understanding the implications of a particular linear-programming model.It is often possible to solve the related linear program with the shadow prices as the variables in place of, or in conjunctionwith, the original linear program, thereby taking advantage of some computational efﬁciencies.Understanding the dual problem leads to specialized algorithms for some important classes of linear programming problems. Examples include the transportation simplex method, the Hungarian algorithm for the assignment problem, and the network simplex method. Even column generation relies partly on duality.The dual can be helpful for sensitivity analysis.Changing the primal's right-hand side constraint vector or adding a new constraint to it can make the original primal optimal solution infeasible. However, this only changes the objective function or adds a new variable to the dual, respectively, so the original dual optimal solution is still feasible (and is usually not far from the new dual optimal solution).Sometimes finding an initial feasible solution to the dual is much easier than finding one for the primal. For example, if the primal is a minimization problem, the constraints are often of the form , , for . The dual constraints would then likely be of the form , , for . The origin is feasible for the latter problem but not for the former.The dual variables give the shadow prices for the primal constraints. Suppose you have a profit maximization problem with a resource constraint . Then the value of the corresponding dual variable in the optimal solution tells you that you get an increase of in the maximum profit for each unit increase in the amount of resource (absent degeneracy and for small increases in resource ).Sometimes the dual is just easier to solve. Aseem Dua mentions this: A problem with many constraints and few variables can be converted into one with few constraints and many variables.

Your gay

Stone Cold. Robert Swindells