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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 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:
The NumPy numerical library interprets a*b or a.multiply(b) as the Hadamard product, and uses a@b or a.matmul(b) for the matrix product. With the SymPy symbolic library, multiplication of array objects as either a*b or a@b will produce the matrix product. The Hadamard product can be obtained with the method call a.multiply_elementwise(b). [22]
In theoretical computer science, the computational complexity of matrix multiplication dictates how quickly the operation of matrix multiplication can be performed. Matrix multiplication algorithms are a central subroutine in theoretical and numerical algorithms for numerical linear algebra and optimization, so finding the fastest algorithm for matrix multiplication is of major practical ...
A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient than ...
Multiplication (often denoted by the cross symbol ... and is the same as the number of things in an array when the rational numbers happen to be whole numbers. ...
Some programming languages utilize doubly subscripted arrays (or arrays of arrays) to represent an m-by-n matrix. Some programming languages start the numbering of array indexes at zero, in which case the entries of an m -by- n matrix are indexed by 0 ≤ i ≤ m − 1 {\displaystyle 0\leq i\leq m-1} and 0 ≤ j ≤ n − 1 {\displaystyle 0\leq ...
In computer science, Cannon's algorithm is a distributed algorithm for matrix multiplication for two-dimensional meshes first described in 1969 by Lynn Elliot Cannon. [1] [2]It is especially suitable for computers laid out in an N × N mesh. [3]