outer product


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outer product

[¦au̇d·ər ′präd·əkt]
(mathematics)
For any two tensors R and S, a tensor T each of whose indices corresponds to an index of R or an index of S, and each of whose components is the product of the component of R and the component of S with identical values of the corresponding indices.
References in periodicals archive ?
Product Information Management is an exhaustive system that permits an association to store all parts of product information; it covers both inward and outer product information.
The hierarchical geometric structure corresponds to the hierarchical Grassmann structure for the outer product in CGA.
A blade is the outer product of a series of linearly independent vectors.
Using the outer product, the operation is [mathematical expression not reproducible], which is part of A and corresponding to [<A>.
In this paper, we look at the symmetric outer product decomposition (SOPD), a summation of rank-one fully (partially) symmetric tensors.
The outer product of the vectors x, y, z [member of] [R.
Their outer product R(4) describes Minkowskian space-time, whose inner products form bivectors, pseudo-vectors, and pseudo-scalars, describing spin, momentum-energy, and action, respectively, which automatically satisfy the Heisenberg Uncertainty Principle.
Using the standard modules of the library of CAS REDUCE (for example, a matrices product subprogram, a matrices determinant subprogram, a matrix inversion subprogram) and several nonstandard algorithms as the matrices elements cofactor, a matrices determinant cross-expansion and a matrices outer product we deduced the symbolic expressions of coefficients of the geometric properties, material matrices and global stiffness matrices of the following types of the finite elements:
The original approach in all procedures was that the outer product of a shape functions matrices was used on the element stiffness matrix as well as the full anisotropy and polynomial representation of elasticity constants in the material matrix.
5 [micro]L outer product and NP- 1 as 1 primer and NP1 s2 (5'-CTCACCTGCGAGCTCTGTAAGTA) primer was performed at an annealing temperature of 55[degrees]C.
The coextruder is a single-screw machine, which, in accordance with the requirements of each application, plastifies the virgin PET necessary for the outer product layers.
The outer product inside the cans is over-processed due to slow heating of the center, causing poor quality and taste.