expkB
expkB is a mathematical shorthand denoting the matrix exponential of k times a square matrix B, written as exp(kB) or e^(kB). It is a central object in linear algebra, differential equations, and theoretical physics, where B often represents a linear operator or a rate/generator matrix.
Definition and computation: exp(kB) is defined by the power series exp(kB) = sum_{n=0}^∞ (k^n B^n)/n!. If B
Key properties: exp(0) = I, and the derivative with respect to k satisfies d/dk exp(kB) = B exp(kB)
Applications: In solving linear systems dx/dt = Bx, the solution is x(t) = exp(tB) x(0). In physics, exp(-iHt/ħ)
See also: matrix exponential, Jordan form, scaling and squaring, Padé approximants.