multilinear map उदाहरण वाक्य

उदाहरण वाक्य

1. The second Cayley hyperdeterminant originated in 1845 and is often called " Det . " This definition is a discriminant for a singular point on a scalar valued multilinear map.
2. I wonder if there's an elementary proof that a multilinear map with multiple arguments cannot be simultaneously linear in all of them unless it's the zero map, as stated in the article.
3. The notion of "'alternatization "'( or "'alternatisation "'in British English ) is used to derive an alternating multilinear map from any multilinear map with all arguments belonging to the same space.
4. The notion of "'alternatization "'( or "'alternatisation "'in British English ) is used to derive an alternating multilinear map from any multilinear map with all arguments belonging to the same space.
5. The set of all such multilinear maps forms a vector space, called the tensor product space of type \ left ( r, \, s \ right ) at p and denoted by \ left ( T _ p \ right ) ^ r _ sM.
6. In viewing a tensor as a multilinear map, it is conventional to identify the vector space " V " with the space of linear functionals on the dual of " V ", the double dual " V "  "  ".
7. At p, these two vector spaces may be used to construct type \ left ( r, \, s \ right ) tensors, which are real-valued multilinear maps acting on the direct sum of r copies of the cotangent space with s copies of the tangent space.
8. In the general case a hyperdeterminant is defined as a discriminant for a multilinear map " f " from finite-dimensional vector spaces " V " i to their underlying field " K " which may be \ mathbb { R } or \ mathbb { C }.
9. More generally, a tensor of order " m " which takes in " n " vectors ( where " n " is between 0 and " m " inclusive ) will return a tensor of order, see Tensor : As multilinear maps for further generalizations and details.