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  2. Matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication

    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.

  3. Hadamard product (matrices) - Wikipedia

    en.wikipedia.org/wiki/Hadamard_product_(matrices)

    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.

  4. Matrix multiplication algorithm - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication...

    Matrix multiplication completed in 2n-1 steps for two n×n matrices on a cross-wired mesh. There are a variety of algorithms for multiplication on meshes . For multiplication of two n × n on a standard two-dimensional mesh using the 2D Cannon's algorithm , one can complete the multiplication in 3 n -2 steps although this is reduced to half ...

  5. Wallace tree - Wikipedia

    en.wikipedia.org/wiki/Wallace_tree

    As making the partial products is () and the final addition is (⁡), the total multiplication is (⁡), not much slower than addition. From a complexity theoretic perspective, the Wallace tree algorithm puts multiplication in the class NC 1. The downside of the Wallace tree, compared to naive addition of partial products, is its much higher ...

  6. Outer product - Wikipedia

    en.wikipedia.org/wiki/Outer_product

    More generally, given two tensors (multidimensional arrays of numbers), their outer product is a tensor. The outer product of tensors is also referred to as their tensor product, and can be used to define the tensor algebra. The outer product contrasts with:

  7. Computational complexity of matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Computational_complexity...

    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 ...

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