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Elements that occur more than / times in a multiset of size may be found by a comparison-based algorithm, the Misra–Gries heavy hitters algorithm, in time (). The element distinctness problem is a special case of this problem where k = n {\displaystyle k=n} .
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.
Hadamard's maximal determinant problem, named after Jacques Hadamard, asks for the largest determinant of a matrix with elements equal to 1 or −1. The analogous question for matrices with elements equal to 0 or 1 is equivalent since, as will be shown below, the maximal determinant of a {1,−1} matrix of size n is 2 n−1 times the maximal determinant of a {0,1} matrix of size n−1.
The Casimir element for B is the element of the universal enveloping algebra given by the formula Ω = ∑ i = 1 n X i X i . {\displaystyle \Omega =\sum _{i=1}^{n}X_{i}X^{i}.} Although the definition relies on a choice of basis for the Lie algebra, it is easy to show that Ω is independent of this choice.
Formally, a parity check matrix H of a linear code C is a generator matrix of the dual code, C ⊥. This means that a codeword c is in C if and only if the matrix-vector product Hc ⊤ = 0 (some authors [1] would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations. [2]
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Bowers also has a shot at the most yards for a season by a rookie tight end — Mike Ditka's 1.076 during the 1961 season. But he might have to pick up his production a bit to overtake that mark ...
Susie Coughlin was concerned when her daughter struggled with reading skills at her public school.. The mom of two was disappointed her district didn't teach phonics as part of its literacy program.