Search Results for ""

Let A be a sum of squares of n independent normal standardized variates X_i, and suppose A=B+C where B is a quadratic form in the x_i, distributed as chi-squared with h ...

Two variates A and B are statistically independent iff the conditional probability P(A|B) of A given B satisfies P(A|B)=P(A), (1) in which case the probability of A and B is ...

A maximum irredundant set is an irredundant set of largest possible size in a graph. Note that a maximum irredundant set is not equivalent to a maximal irredundant set, which ...

If two square n×n matrices A and B are simultaneously upper triangularizable by similarity transforms, then there is an ordering a_1, ..., a_n of the eigenvalues of A and ...

A minimal edge cover is an edge cover of a graph that is not a proper subset of any other edge cover. Every minimum edge cover is a minimal edge cover, but the converse does ...

A minimal vertex cut is an vertex cut of a graph that is not a proper subset of any other vertex cut. Every minimum vertex cut is a minimal vertex cut, but the converse does ...

A minimum dominating set is a dominating set of smallest size in a given graph. The size of a minimum dominating set is known as the domination number of the graph. A minimum ...

The sum of the first n odd numbers is a square number, sum_(k=1)^n(2k-1)=n^2. A sort of converse also exists, namely the difference of the nth and (n-1)st square numbers is ...

Variables x_i and x_j are said to be uncorrelated if their covariance is zero: cov(x_i,x_j)=0. Independent statistics are always uncorrelated, but the converse is not ...

Vorobiev's theorem states that if F_l^2|F_k, then F_l|k, where F_n is a Fibonacci number and a|b means a divides b. The theorem was discovered by Vorobiev in 1942, but not ...