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For example, for the 2×2 matrix = [], the vectorization is = []. The connection between the vectorization of A and the vectorization of its transpose is given by the commutation matrix . Compatibility with Kronecker products
The cross product operation is an example of a vector rank function because it operates on vectors, not scalars. Matrix multiplication is an example of a 2-rank function, because it operates on 2-dimensional objects (matrices). Collapse operators reduce the dimensionality of an input data array by one or more dimensions. For example, summing ...
Array programming, a style of computer programming where operations are applied to whole arrays instead of individual elements; Automatic vectorization, a compiler optimization that transforms loops to vector operations
Python sets are very much like mathematical sets, and support operations like set intersection and union. Python also features a frozenset class for immutable sets, see Collection types. Dictionaries (class dict) are mutable mappings tying keys and corresponding values. Python has special syntax to create dictionaries ({key: value})
Automatic vectorization, in parallel computing, is a special case of automatic parallelization, where a computer program is converted from a scalar implementation, which processes a single pair of operands at a time, to a vector implementation, which processes one operation on multiple pairs of operands at once.
A graph of the vector-valued function r(z) = 2 cos z, 4 sin z, z indicating a range of solutions and the vector when evaluated near z = 19.5. A common example of a vector-valued function is one that depends on a single real parameter t, often representing time, producing a vector v(t) as the result.
In natural language processing, a sentence embedding is a representation of a sentence as a vector of numbers which encodes meaningful semantic information. [1] [2 ...
Examples of its use include sparse linear algebra operations, [1] sorting algorithms, fast Fourier transforms, [2] and some computational graph theory problems. [3] It is the vector equivalent of register indirect addressing , with gather involving indexed reads, and scatter, indexed writes.