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## what is the simplified form of ? assume x ≠ 0.

### Matrix Exponential - Wikipedia

Web In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group.. Let X be an n×n real or …

### Central Limit Theorem - Wikipedia

Web In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.. The theorem is a key concept in probability theory because it implies that …

### ECMAScript Language Specification - ECMA-262 Edition 5.1

Web The mathematical function sign(x) yields 1 if x is positive and −1 if x is negative. The sign function is not used in this standard for cases when x is zero. The notation “ x modulo y ” (y must be finite and nonzero) computes a value k of the same sign as y (or zero) such that abs(k) < abs(y) and x−k = q × y for some integer q.

### Non-Hermitian Topological Whispering Gallery | Nature

Web 29/9/2021 · Understanding topological phases in non-Hermitian settings has become a thriving area in many research fields such as condensed-matter physics, cold atoms physics, and classical optics and acoustics.

### List Of Logarithmic Identities - Wikipedia

Web We can then get 10 9,808,357 × 10 0.09543 ≈ 1.25 × 10 9,808,357. Similarly, factorials can be approximated by summing the logarithms of the terms. Complex logarithm identities. The complex logarithm is the complex number analogue of the logarithm function. No single valued function on the complex plane can satisfy the normal rules for ...

### Spacetime - Wikipedia

Web In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive differently where and when events occur.. Until the 20th century, it was …

### Möbius Transformation - Wikipedia

Web 1) for each A ∈ SL(2, C), and this action of SL(2, C) preserves the determinant of X because det A = 1 . Since the determinant of X is identified with the quadratic form Q , SL(2, C) acts by Lorentz transformations. On dimensional grounds, SL(2, C) covers a neighborhood of the identity of SO(1,3). Since SL(2, C) is connected, it covers the entire restricted Lorentz …

### Mann–Whitney U Test - Wikipedia

Web In statistics, the Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW/MWU), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric test of the null hypothesis that, for randomly selected values X and Y from two populations, the probability of X being greater than Y is equal to the probability of Y being greater than X.

### Solving Logarithmic Functions – Explanation & Examples

Web An exponent is a form of writing the repeated multiplication of a number by itself. An exponential function is of the form f (x) = b y, where b > 0 < x and b ≠ 1. The quantity x is the number, b is the base, and y is the exponent or …

### Ordinary Differential Equation - Wikipedia

Web In general, F is a function of the position x(t) of the particle at time t. The unknown function x(t) appears on both sides of the differential equation, and is indicated in the notation F(x(t)). Definitions. In what follows, let y be a dependent variable and x an independent variable, and y = f(x) is an unknown function of x.

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