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  2. Matrix representation - Wikipedia

    en.wikipedia.org/wiki/Matrix_representation

    An m × n (read as m by n) order matrix is a set of numbers arranged in m rows and n columns. Matrices of the same order can be added by adding the corresponding elements. Two matrices can be multiplied, the condition being that the number of columns of the first matrix is equal to the number of rows of the second matrix.

  3. Matrix addition - Wikipedia

    en.wikipedia.org/wiki/Matrix_addition

    In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together. For a vector , v → {\displaystyle {\vec {v}}\!} , adding two matrices would have the geometric effect of applying each matrix transformation separately onto v → {\displaystyle {\vec {v}}\!} , then adding the transformed vectors.

  4. Matrix Template Library - Wikipedia

    en.wikipedia.org/wiki/Matrix_Template_Library

    The Matrix Template Library (MTL) is a linear algebra library for C++ programs. The MTL uses template programming , which considerably reduces the code length. All matrices and vectors are available in all classical numerical formats: float , double , complex<float> or complex<double> .

  5. Strassen algorithm - Wikipedia

    en.wikipedia.org/wiki/Strassen_algorithm

    The following exposition of the algorithm assumes that all of these matrices have sizes that are powers of two (i.e., ,, ⁡ ()), but this is only conceptually necessary — if the matrices , are not of type , the "missing" rows and columns can be filled with zeros to obtain matrices with sizes of powers of two — though real implementations ...

  6. Addition - Wikipedia

    en.wikipedia.org/wiki/Addition

    Matrix addition is defined for two matrices of the same dimensions. The sum of two m × n (pronounced "m by n") matrices A and B, denoted by A + B, is again an m × n matrix computed by adding corresponding elements: [75] [76]

  7. 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 ...

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  9. Expression templates - Wikipedia

    en.wikipedia.org/wiki/Expression_templates

    Consider a library representing vectors and operations on them. One common mathematical operation is to add two vectors u and v, element-wise, to produce a new vector.The obvious C++ implementation of this operation would be an overloaded operator+ that returns a new vector object: