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The nullity of a graph in the mathematical subject of graph theory can mean either of two unrelated numbers. If the graph has n vertices and m edges, then: In the matrix theory of graphs, the nullity of the graph is the nullity of the adjacency matrix A of the graph. The nullity of A is given by n − r where r is the rank of the adjacency
The nullity of a matrix is the dimension of the null space, and is equal to the number of columns in the reduced row echelon form that do not have pivots. [7] The rank and nullity of a matrix A with n columns are related by the equation:
The run test is based on the null hypothesis that each element in the sequence is independently drawn from the same distribution. Under the null hypothesis, the number of runs in a sequence of N elements [ note 1 ] is a random variable whose conditional distribution given the observation of N + positive values [ note 2 ] and N − negative ...
Rank–nullity theorem. The rank–nullity theorem is a theorem in linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity of M; and; the dimension of the domain of a linear transformation f is the sum of the rank of f (the dimension of the image of f) and the nullity of f (the dimension of ...
Analogously, the nullity of the graph is the nullity of its oriented incidence matrix, given by the formula m − n + c, where n and c are as above and m is the number of edges in the graph. The nullity is equal to the first Betti number of the graph. The sum of the rank and the nullity is the number of edges.
Nullity (linear algebra), the dimension of the kernel of a mathematical operator or null space of a matrix; Nullity (graph theory), the nullity of the adjacency matrix of a graph; Nullity, the difference between the size and rank of a subset in a matroid; Nullity, a concept in transreal arithmetic denoted by Φ, or similarly in wheel theory ...
Of all probability distributions with a given entropy, the one whose Fisher information matrix has the smallest trace is the Gaussian distribution. This is like how, of all bounded sets with a given volume, the sphere has the smallest surface area.
As opposed to that, the false positive rate is associated with a post-prior result, which is the expected number of false positives divided by the total number of hypotheses under the real combination of true and non-true null hypotheses (disregarding the "global null" hypothesis). Since the false positive rate is a parameter that is not ...