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In mathematics, especially in linear algebra and matrix theory, the vectorization of a matrix is a linear transformation which converts the matrix into a vector.
Automatic vectorization, a compiler optimization that transforms loops to vector operations; Image tracing, the creation of vector from raster graphics; Word embedding, mapping words to vectors, in natural language processing
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.
Vectorization is also used to recover information that was originally in a vector format but has been lost or has become unavailable. A company may have commissioned a logo from a graphic arts firm. Although the graphics firm used a vector format, the client company may not have received a copy of that format.
If one views any real m × n matrix as a vector of length mn (an operation called vectorization) then the above operation on A and B coincides with the standard dot product. According to the above expression, tr(A ⊤ A) is a sum of squares and hence is nonnegative, equal to zero if and only if A is zero.
The fundamental idea behind array programming is that operations apply at once to an entire set of values. This makes it a high-level programming model as it allows the programmer to think and operate on whole aggregates of data, without having to resort to explicit loops of individual scalar operations.
Vectorization of a Kronecker product: Let A {\displaystyle A} be an m × n {\displaystyle m\times n} matrix and B {\displaystyle B} a p × q {\displaystyle p\times q} matrix. When the order of the Kronecker product and vectorization is interchanged, the two operations can be linked linearly through a function that involves the commutation ...
Single instruction, multiple data. Single instruction, multiple data (SIMD) is a type of parallel processing in Flynn's taxonomy.SIMD can be internal (part of the hardware design) and it can be directly accessible through an instruction set architecture (ISA), but it should not be confused with an ISA.