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Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication.
Download as PDF; Printable version; In other projects ... Pages in category "Operations on vectors" The following 16 pages are in this category, out of 16 total ...
For a symmetric matrix A, the vector vec(A) contains more information than is strictly necessary, since the matrix is completely determined by the symmetry together with the lower triangular portion, that is, the n(n + 1)/2 entries on and below the main diagonal. For such matrices, the half-vectorization is sometimes more useful than the ...
The dotted vector, in this case B, is differentiated, while the (undotted) A is held constant. The utility of the Feynman subscript notation lies in its use in the derivation of vector and tensor derivative identities, as in the following example which uses the algebraic identity C⋅(A×B) = (C×A)⋅B:
A free vector is a vector quantity having an undefined support or region of application; it can be freely translated with no consequences; a displacement vector is a prototypical example of free vector. Aside from the notion of units and support, physical vector quantities may also differ from Euclidean vectors in terms of metric.
Since any signal vector that resides in the signal subspace must be orthogonal to the noise subspace, , it must be that for all the eigenvectors {} = + that spans the noise subspace. In order to measure the degree of orthogonality of e {\displaystyle \mathbf {e} } with respect to all the v i ∈ U N {\displaystyle \mathbf {v} _{i}\in {\mathcal ...
In modern mathematics, the presentation through vector spaces is generally preferred, since it is more synthetic, more general (not limited to the finite-dimensional case), and conceptually simpler, although more abstract. A vector space over a field F (often the field of the real numbers) is a set V equipped with two binary operations.
It is the vector equivalent of register indirect addressing, with gather involving indexed reads, and scatter, indexed writes. Vector processors (and some SIMD units in CPUs ) have hardware support for gather and scatter operations, as do many input/output systems, allowing large data sets to be transferred to main memory more rapidly.