“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.
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