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Stack Overflow is a question-and-answer website for computer programmers. It is the flagship site of the Stack Exchange Network . [ 2 ] [ 3 ] [ 4 ] It was created in 2008 by Jeff Atwood and Joel Spolsky .
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:
Matrix multiplication shares some properties with usual multiplication. However, matrix multiplication is not defined if the number of columns of the first factor differs from the number of rows of the second factor, and it is non-commutative, [10] even when the product remains defined after changing the order of the factors. [11] [12]
The matrix chain multiplication problem generalizes to solving a more abstract problem: given a linear sequence of objects, an associative binary operation on those objects, and a way to compute the cost of performing that operation on any two given objects (as well as all partial results), compute the minimum cost way to group the objects to ...
The Hadamard product operates on identically shaped matrices and produces a third matrix of the same dimensions. In mathematics, the Hadamard product (also known as the element-wise product, entrywise product [1]: ch. 5 or Schur product [2]) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding elements.
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).
The fused multiply–add operation was introduced as "multiply–add fused" in the IBM POWER1 (1990) processor, [14] but has been added to numerous other processors since then: HP PA-8000 (1996) and above; Hitachi SuperH SH-4 (1998) SCE-Toshiba Emotion Engine (1999) Intel Itanium (2001) STI Cell (2006) Fujitsu SPARC64 VI (2007) and above
In PHP, it is used just before an expression to make the interpreter suppress errors that would be generated from that expression. [33] In Python 2.4 and up, it is used to decorate a function (wrap the function in another one at creation time). In Python 3.5 and up, it is also used as an overloadable matrix multiplication operator. [34]