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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 ...
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
7.5 Exponential and logarithms. 8 See also. 9 Notes. ... The following is a useful property to calculate low-integer-order polylogarithms recursively in closed form:
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 ...
The fractional Schrödinger equation, a fundamental equation of fractional quantum mechanics, has the following form: [73] [74] (,) = (,) + (,) (,). where the solution of the equation is the wavefunction ψ ( r , t ) – the quantum mechanical probability amplitude for the particle to have a given position vector r at any given time t , and ħ ...
A first-order homogeneous matrix ordinary differential equation in two functions x(t) and y(t), when taken out of matrix form, has the following form: d x d t = a 1 x + b 1 y , d y d t = a 2 x + b 2 y {\displaystyle {\frac {dx}{dt}}=a_{1}x+b_{1}y,\quad {\frac {dy}{dt}}=a_{2}x+b_{2}y}
The 9-person Symbolab team, based in Tel Aviv, will join Course Hero . The platforms will live under independent branding for the near future, according to Andrew Grauer, CEO of Course Hero.
Similar asymptotic analysis is possible for exponential generating functions; with an exponential generating function, it is a n / n! that grows according to these asymptotic formulae. Generally, if the generating function of one sequence minus the generating function of a second sequence has a radius of convergence that is larger than ...