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The matrix exponential satisfies the following properties. [2] We begin with the properties that are immediate consequences of the definition as a power series: e 0 = I; exp(X T) = (exp X) T, where X T denotes the transpose of X. exp(X ∗) = (exp X) ∗, where X ∗ denotes the conjugate transpose of X. If Y is invertible then e YXY −1 = Ye ...
MATLAB's powermod function from Symbolic Math Toolbox; Wolfram Language has the PowerMod function; Perl's Math::BigInt module has a bmodpow() method to perform modular exponentiation; Raku has a built-in routine expmod. Go's big.Int type contains an Exp() (exponentiation) method whose third parameter, if non-nil, is the modulus
In probability theory, an exponentially modified Gaussian distribution (EMG, also known as exGaussian distribution) describes the sum of independent normal and exponential random variables. An exGaussian random variable Z may be expressed as Z = X + Y, where X and Y are independent, X is Gaussian with mean μ and variance σ 2, and Y is ...
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
The exponential of a variable is denoted or , with the two notations used interchangeably. It is called exponential because its argument can be seen as an exponent to which a constant number e ≈ 2.718, the base, is raised. There are several other definitions of the exponential function, which are all equivalent ...
MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities.
In mathematics, exponentiation, denoted b n, is an operation involving two numbers: the base, b, and the exponent or power, n. [1] When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b n is the product of multiplying n bases: [1] = ⏟.
are the exponential map and inverse exponential map, respectively, "exp" and "log" denote the ordinary matrix exponential and matrix logarithm, and E[·] is the ordinary expectation operator defined on a vector space, in this case the tangent space of the manifold. [1]