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The possible values of X i form a countable set S called the state space of the chain. [1] Markov chains are often described by a sequence of directed graphs, where the edges of graph n are labeled by the probabilities of going from one state at time n to the other states at time n + 1, (+ = =).
In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical object. [1] [2] Equality between A and B is written A = B, and pronounced "A equals B". In this equality, A and B are distinguished by calling them left-hand side (LHS), and right-hand side ...
Given an n × n square matrix A of real or complex numbers, an eigenvalue λ and its associated generalized eigenvector v are a pair obeying the relation [1] =,where v is a nonzero n × 1 column vector, I is the n × n identity matrix, k is a positive integer, and both λ and v are allowed to be complex even when A is real.l When k = 1, the vector is called simply an eigenvector, and the pair ...
That is, the array starts at 1 (the initial value), increments with each step from the previous value by 2 (the increment value), and stops once it reaches (or is about to exceed) 9 (the terminator value). The increment value can actually be left out of this syntax (along with one of the colons), to use a default value of 1. >>
A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. [1] ... ch. 1-3 One ...
Linear interpolation on a data set (red points) consists of pieces of linear interpolants (blue lines). Linear interpolation on a set of data points (x 0, y 0), (x 1, y 1), ..., (x n, y n) is defined as piecewise linear, resulting from the concatenation of linear segment interpolants between each pair of data points.
The record may be time-dependent (e.g. rainfall measured in one spot) or space-dependent (e.g. crop yields in an area) or otherwise. The cumulative frequency M Xr of a reference value Xr is the frequency by which the observed values X are less than or equal to Xr. The relative cumulative frequency Fc can be calculated from:
The spectral radius of a finite graph is defined to be the spectral radius of its adjacency matrix.. This definition extends to the case of infinite graphs with bounded degrees of vertices (i.e. there exists some real number C such that the degree of every vertex of the graph is smaller than C).