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If a matrix A has a matrix of eigenvectors P that is not invertible (for example, the matrix [1 1; 0 1] has the noninvertible system of eigenvectors [1 0; 0 0]), then A does ...

The Stieltjes integral is a generalization of the Riemann integral. Let f(x) and alpha(x) be real-valued bounded functions defined on a closed interval [a,b]. Take a ...

A stochastic matrix, also called a probability matrix, probability transition matrix, transition matrix, substitution matrix, or Markov matrix, is matrix used to characterize ...

A temporal point process is a random process whose realizations consist of the times {tau_j}_(j in J) of isolated events. Note that in some literature, the values tau_j are ...

A universal differential equation (UDE) is a nontrivial differential-algebraic equation with the property that its solutions approximate to arbitrary accuracy any continuous ...

Voronin (1975) proved the remarkable analytical property of the Riemann zeta function zeta(s) that, roughly speaking, any nonvanishing analytic function can be approximated ...

Simply stated, floating-point arithmetic is arithmetic performed on floating-point representations by any number of automated devices. Traditionally, this definition is ...

If the section function of a centered convex body in n-dimensional Euclidean space (n>=3) is smaller than that of another such body, is its volume also smaller? The solution ...

There are no fewer than two closely related but somewhat different notions of gerbe in mathematics. For a fixed topological space X, a gerbe on X can refer to a stack of ...

If P be a point in the plane of an equilateral triangle DeltaABC, then the lengths of line segments AP, BP, and CP correspond the sides of a triangle, which is degenerate ...