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  2. 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 ...

  3. Matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication

    For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB. [1]

  4. Kronecker product - Wikipedia

    en.wikipedia.org/wiki/Kronecker_product

    In mathematics, the Kronecker product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix.It is a specialization of the tensor product (which is denoted by the same symbol) from vectors to matrices and gives the matrix of the tensor product linear map with respect to a standard choice of basis.

  5. Khatri–Rao product - Wikipedia

    en.wikipedia.org/wiki/Khatri–Rao_product

    In mathematics, the Khatri–Rao product or block Kronecker product of two partitioned matrices and is defined as [1] [2] [3] = in which the ij-th block is the m i p i × n j q j sized Kronecker product of the corresponding blocks of A and B, assuming the number of row and column partitions of both matrices is equal.

  6. Computational complexity of matrix multiplication - Wikipedia

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

    The matrix multiplication exponent, usually denoted ω, is the smallest real number for which any two matrices over a field can be multiplied together using + field operations. This notation is commonly used in algorithms research, so that algorithms using matrix multiplication as a subroutine have bounds on running time that can update as ...

  7. Basic Linear Algebra Subprograms - Wikipedia

    en.wikipedia.org/wiki/Basic_Linear_Algebra...

    The Library for Accelerated Math Applications is a C++ template library for writing numerical solvers targeting various kinds of hardware (e.g. GPUs through CUDA or OpenCL) on distributed memory systems, hiding the hardware specific programming from the program developer MTL4 The Matrix Template Library version 4 is a generic C++ template ...

  8. Matrix chain multiplication - Wikipedia

    en.wikipedia.org/wiki/Matrix_chain_multiplication

    A is a 10×30 matrix, B is a 30×5 matrix, C is a 5×60 matrix, and the final result is a 10×60 matrix. The regular polygon for this example is a 4-gon, i.e. a square: The matrix product AB is a 10x5 matrix and BC is a 30x60 matrix. The two possible triangulations in this example are:

  9. Comparison of linear algebra libraries - Wikipedia

    en.wikipedia.org/wiki/Comparison_of_linear...

    C++ template library; binds to optimized BLAS such as the Intel MKL; Includes matrix decompositions, non-linear solvers, and machine learning tooling Eigen: Benoît Jacob C++ 2008 3.4.0 / 08.2021 Free MPL2: Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. Fastor [5]