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The Gram matrix of any orthonormal basis is the identity matrix. Equivalently, the Gram matrix of the rows or the columns of a real rotation matrix is the identity matrix. Likewise, the Gram matrix of the rows or columns of a unitary matrix is the identity matrix. The rank of the Gram matrix of vectors in or equals the dimension of the space ...
(B) (,) of weight = and minimal order exist if is a prime power and such a circulant weighing matrix can be obtained by signing the complement of a finite projective plane. Since all C W ( n , k ) {\displaystyle CW(n,k)} for k ≤ 25 {\displaystyle k\leq 25} have been classified, the first open case is C W ( 105 , 36 ) {\displaystyle CW(105,36)} .
Outcome: Weight increases; Calories consumed < Calories expended. Also known as Negative Energy Balance; Outcome: Weight decreases [9] The calories a person consumes come from food and drink intake. [9] The calories a person expends comes from their basal metabolic rate and their daily physical activity. [5]
Nutripoints [9] is a food-rating system which places foods on a numerical scale based on their overall nutritional value. The method is based on an analysis of 26 positive factors (such as vitamins, minerals, protein and fiber) and negative factors (such as cholesterol, saturated fat, sugar and sodium) relative to calories.
so is a Gram matrix over the distributions from which the training data are sampled. Finding an orthogonal transform onto a low-dimensional subspace B (in the feature space) which minimizes the distributional variance, DICA simultaneously ensures that B aligns with the bases of a central subspace C for which Y {\displaystyle Y} becomes ...
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Based on the work of Atwater, it became common practice to calculate energy content of foods using 4 kcal/g for carbohydrates and proteins and 9 kcal/g for lipids. [2] The system was later improved by Annabel Merrill and Bernice Watt of the USDA, who derived a system whereby specific calorie conversion factors for different foods were proposed. [3]
The mean-squared density matrices, representing deviation from the true density matrix, may be rewritten as a Gram matrix, and an iterative algorithm is used to minimize the Gram matrix and solve the QP. [17] [6]