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The matrix exponential of another matrix (matrix-matrix exponential), [24] is defined as = = for any normal and non-singular n×n matrix X, and any complex n×n matrix Y. For matrix-matrix exponentials, there is a distinction between the left exponential Y X and the right exponential X Y , because the multiplication operator for matrix ...
In probability theory, the matrix-exponential distribution is an absolutely continuous distribution with rational Laplace–Stieltjes transform. [1] They were first introduced by David Cox in 1955 as distributions with rational Laplace–Stieltjes transforms .
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Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide ... Template documentation. Use one of the following depending ...
The exponential of a matrix A is defined by =!. Given a matrix B, another matrix A is said to be a matrix logarithm of B if e A = B.. Because the exponential function is not bijective for complex numbers (e.g. = =), numbers can have multiple complex logarithms, and as a consequence of this, some matrices may have more than one logarithm, as explained below.
In mathematics, every analytic function can be used for defining a matrix function that maps square matrices with complex entries to square matrices of the same size.. This is used for defining the exponential of a matrix, which is involved in the closed-form solution of systems of linear differential equations.
The ordinary exponential function of mathematical analysis is a special case of the exponential map when is the multiplicative group of positive real numbers (whose Lie algebra is the additive group of all real numbers). The exponential map of a Lie group satisfies many properties analogous to those of the ordinary exponential function, however ...
For a matrix Lie group (,) the Lie algebra is the tangent space of the identity I, and the commutator is simply [X, Y] = XY − YX; the exponential map is the standard exponential map of matrices, = = =!.