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This is a matrix such that () = holds for all {,}, where the message is viewed as a row vector and the vector-matrix product is understood in the vector space over the finite field. In particular, an equivalent way to write the inner product definition for the Hadamard code arises by using the generator matrix whose columns consist of all ...
ATPG (acronym for both automatic test pattern generation and automatic test pattern generator) is an electronic design automation method or technology used to find an input (or test) sequence that, when applied to a digital circuit, enables automatic test equipment to distinguish between the correct circuit behavior and the faulty circuit behavior caused by defects.
The set of Toeplitz matrices is a subspace of the vector space of matrices (under matrix addition and scalar multiplication). Two Toeplitz matrices may be added in O ( n ) {\displaystyle O(n)} time (by storing only one value of each diagonal) and multiplied in O ( n 2 ) {\displaystyle O(n^{2})} time.
In other words, the matrix of the combined transformation A followed by B is simply the product of the individual matrices. When A is an invertible matrix there is a matrix A −1 that represents a transformation that "undoes" A since its composition with A is the identity matrix. In some practical applications, inversion can be computed using ...
A generator matrix for a linear [,,]-code has format , where n is the length of a codeword, k is the number of information bits (the dimension of C as a vector subspace), d is the minimum distance of the code, and q is size of the finite field, that is, the number of symbols in the alphabet (thus, q = 2 indicates a binary code, etc.).
The soft-margin support vector machine described above is an example of an empirical risk minimization (ERM) algorithm for the hinge loss. Seen this way, support vector machines belong to a natural class of algorithms for statistical inference, and many of its unique features are due to the behavior of the hinge loss.
Let A be a square n × n matrix with n linearly independent eigenvectors q i (where i = 1, ..., n).Then A can be factored as = where Q is the square n × n matrix whose i th column is the eigenvector q i of A, and Λ is the diagonal matrix whose diagonal elements are the corresponding eigenvalues, Λ ii = λ i.
The computer graphics pipeline, also known as the rendering pipeline, or graphics pipeline, is a framework within computer graphics that outlines the necessary procedures for transforming a three-dimensional (3D) scene into a two-dimensional (2D) representation on a screen. [1]