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The vectorization is frequently used together with the Kronecker product to express matrix multiplication as a linear transformation on matrices. In particular, = for matrices A, B, and C of dimensions k×l, l×m, and m×n.
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 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 ...
Vectorization (mathematics), a linear transformation that converts a matrix into a column vector; Vector autoregression, an econometric model used to capture the evolution and the interdependencies between multiple time series; Vector boson, a boson with the spin quantum number equal to 1
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.
This is known as vectorization, and is analogous to vectorization of matrices. A standard choice of bijection ...
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.