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单词 power
释义

power

(of a matrix) If A is a square matrix, then the products AA, AAA, AAAA,… are defined, and these powers of A are denoted by A2, A3, A4,…. For all positive integers p and q,

By definition, A0 =  I. Moreover, if A is invertible, then A2, A3,…are invertible, and it can be shown that (A−1)p is the inverse of Ap, so that (A−1)p =  (Ap)−1. So either of these is denoted by A−p. Thus, when A is invertible, Ap has been defined for all integers and properties (i) and (ii) above hold for all integers p and q.

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更新时间:2025/4/29 3:56:53