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The permanent is defined similarly to the determinant, as a sum of products of sets of matrix entries that lie in distinct rows and columns. However, where the determinant weights each of these products with a ±1 sign based on the parity of the set, the permanent weights them all with a +1 sign.
Laplace's expansion by minors for computing the determinant along a row, column or diagonal extends to the permanent by ignoring all signs. [9]For every , = =,,,where , is the entry of the ith row and the jth column of B, and , is the permanent of the submatrix obtained by removing the ith row and the jth column of B.
The compression set (ASTM D395) of a material is the permanent deformation remaining after compressing it. [1] In specific methods, temperatures and percent compression are specified. The term is normally applied to soft materials such as elastomers and foams. Compression is normally measured in two ways: compression set A and compression set B ...
The hafnian of a symmetric matrix is defined as = {,},, where is the set of all partitions of the set {,, …,} into subsets of size . [2] [3]This definition is similar to that of the Pfaffian, but differs in that the signatures of the permutations are not taken into account.
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
You maintain a permanent domicile in Nevada with no intent to return to a previous home state. You spend the majority of your time in Nevada, though no set number of days is explicitly required.
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A partition of a set X is a set of non-empty subsets of X such that every element x in X is in exactly one of these subsets [2] (i.e., the subsets are nonempty mutually disjoint sets). Equivalently, a family of sets P is a partition of X if and only if all of the following conditions hold: [3]