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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 ...
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]
[1] [2] The large calorie, food calorie, dietary calorie, kilocalorie, or kilogram calorie is defined as the amount of heat needed to raise the temperature of one liter of water by one degree Celsius (or one kelvin). [1] [3] The small calorie or gram calorie is defined as the amount of heat needed to cause the same increase in one milliliter of ...
The temperature change in the water is then accurately measured with a thermometer. This reading, along with a bomb factor (which is dependent on the heat capacity of the metal bomb parts), is used to calculate the energy given out by the sample burn. A small correction is made to account for the electrical energy input, the burning fuse, and ...
The notion that "a calorie is a calorie" is related to the idea that weight maintenance is a result of equalizing calorie input and calorie output, [4] and may lead to the practice of calorie restriction. Calorie amounts found on food labels are based on the Atwater system. [5] The accuracy of the system is disputed.
The Gram matrix of a sequence of points ,, …, in k-dimensional space ℝ k is the n×n matrix = of their dot products (here a point is thought of as a vector from 0 to that point): g i j = x i ⋅ x j = ‖ x i ‖ ‖ x j ‖ cos θ {\displaystyle g_{ij}=x_{i}\cdot x_{j}=\|x_{i}\|\|x_{j}\|\cos \theta } , where θ {\displaystyle \theta ...
For example under calorie restriction whole body metabolic rate goes down with increasing levels of restriction, but body temperature also follows the same pattern. By manipulating the ambient temperature and exposure to wind it was shown in mice and hamsters that body temperature is a more important modulator of lifespan than metabolic rate.