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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 ...
with N B and N G being the molarities 1-column matrices of the batch and glass components respectively, and B being the batching matrix. [1] [2] [3] The symbol "T" stands for the matrix transpose operation, "−1" indicates matrix inversion, and the sign "·" means the scalar product.
A moderate energy density would be 1.6 to 3 calories per gram (7–13 kJ/g); salmon, lean meat, and bread would fall in this category. Foods with high energy density have more than three calories per gram (>13 kJ/g) and include crackers, cheese, chocolate, nuts, [10] and fried foods like potato or tortilla chips.
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]
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.
The Harris–Benedict equation (also called the Harris-Benedict principle) is a method used to estimate an individual's basal metabolic rate (BMR).. The estimated BMR value may be multiplied by a number that corresponds to the individual's activity level; the resulting number is the approximate daily kilocalorie intake to maintain current body weight.
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There are gram calories and kilogram calories. One kilogram calorie, which equals one thousand gram calories, often appears capitalised and without a prefix (i.e. Cal) when referring to "dietary calories" in food. [17] It is common to apply metric prefixes to the gram calorie, but not to the kilogram calorie: thus, 1 kcal = 1000 cal = 1 Cal.