Cross product "matrix", then it can be generalized in an arbitrary number of dimensions. In mechanics, for example, the angular velocity can be interpreted either as a pseudovector formula_167 or as a anti-symmetric matrix or skew-symmetric tensor formula_168. In the latter case, the velocity law for a rigid body looks: where Ω is formally defined from the rotation matrix formula_170 associated to body's frame: formula_171 In three-dimensions holds: In quantum mechanics the angular momentum formula_173 is often represented as an anti-symmetric matrix or tensor. More precisely, it is the result of cross product involving position formula_174 and linear momentum formula_111: Since both
Linear belief function is a special type of belief function in the sense that its focal elements are exclusive, parallel sub-hyperplanes over the certainty hyperplane and its mass function is a normal distribution across the sub-hyperplanes. Based on the above geometrical description, Shafer and Liu propose two mathematical representations of a LBF: a wide-sense inner product and a linear functional in the variable space, and as their duals over a hyperplane in the sample space. Monney proposes still another structure called Gaussian hints. Although these representations are mathematically neat, they tend to be unsuitable for knowledge representation in expert systems. A linear belief