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The Gram matrix is symmetric in the case the inner product is real-valued; it is Hermitian in the general, complex case by definition of an inner product. The Gram matrix is positive semidefinite, and every positive semidefinite matrix is the Gramian matrix for some set of vectors. The fact that the Gramian matrix is positive-semidefinite can ...
An "almost" triangular matrix, for example, an upper Hessenberg matrix has zero entries below the first subdiagonal. Hollow matrix: A square matrix whose main diagonal comprises only zero elements. Integer matrix: A matrix whose entries are all integers. Logical matrix: A matrix with all entries either 0 or 1.
The determinant of a lattice is the determinant of the Gram matrix, a matrix with entries (a i, a j), where the elements a i form a basis for the lattice. An integral lattice is unimodular if its determinant is 1 or −1. A unimodular lattice is even or type II if all norms are even, otherwise odd or type I.
Low-rank matrix approximations are essential tools in the application of kernel methods to large-scale learning problems. [ 1 ] Kernel methods (for instance, support vector machines or Gaussian processes [ 2 ] ) project data points into a high-dimensional or infinite-dimensional feature space and find the optimal splitting hyperplane.
An n-gram is a sequence of n adjacent symbols in particular order. [1] The symbols may be n adjacent letters (including punctuation marks and blanks), syllables , or rarely whole words found in a language dataset; or adjacent phonemes extracted from a speech-recording dataset, or adjacent base pairs extracted from a genome.
Clouse, 30, fired Hersey just 30 minutes after he reported the relationship and alleged sexual harassment to county authorities on July 29, he alleges.
The reason may be, at least partly, price. Toledano declined to disclose how much the fragment used for the B/1M cost, but he noted that raw meteorite can sell for more, per gram, than gold.
Jeff Bezos congratulated Donald Trump on winning the presidential election, but they've squabbled over the years.