“exponential of a matrix”的概念、定义、习题解题方法及翻译-数学辞典

单词

exponential of a matrix

释义

exponential of a matrix

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

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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