“exponential of a matrix”的概念、定义、翻译、参考文献-科学参考

exponential of a matrix

Mathematics

Given a square matrix A, its exponential is expA = I + A + A²/2!+A³/3!+···. This series converges in the space of n × n matrices. Further, exp(A + B) = expA expB for commuting matrices A,B, but this identity does not generally hold. Note two simultaneous scalar differential equations dx/dt = 2x + 3y, dy/dt = x−y, can be rewritten as dr/dt = Ar where

$A = (\begin{matrix} 2 & 3 \\ 1 & - 1 \end{matrix}) and r = (\begin{matrix} x \\ y \end{matrix}) .$

The solution then equals r(t) = exp(At)r(0). This matrix exponential also has an important role in the study of Lie groups.

单词	exponential of a matrix
释义	exponential of a matrix Mathematics Given a square matrix A, its exponential is expA = I + A + A²/2!+A³/3!+···. This series converges in the space of n × n matrices. Further, exp(A + B) = expA expB for commuting matrices A,B, but this identity does not generally hold. Note two simultaneous scalar differential equations dx/dt = 2x + 3y, dy/dt = x−y, can be rewritten as dr/dt = Ar where $A = (\begin{matrix} 2 & 3 \\ 1 & - 1 \end{matrix}) and r = (\begin{matrix} x \\ y \end{matrix}) .$ The solution then equals r(t) = exp(At)r(0). This matrix exponential also has an important role in the study of Lie groups.
随便看	biramous biramous appendage birch bird bird of paradise bird of prey birds Birdseye, Clarence (1886–1956) birdseye fabric bireflectance birefringence birefringence chart birefringent filter Birge–Sponer extrapolation Birkeland, Kristian Olaf Bernhard Birkeland–Eyde process Birkhoff, George David Birkhoff, George David (1884–1944) Birkhoff’s completeness theorem Birla Birmingham Solar Oscillations Network Birmingham Wire Gauge Birnbaum inequality Birnbaum, Zygmunt William (1903–2000) Birnbaum–Saunders distribution