“Infinitesimal Matrix Change”的概念、定义、习题解题方法及翻译-数学辞典

单词

Infinitesimal Matrix Change

释义

Infinitesimal Matrix Change

Let B, A, and e be square matrices with e small, and define

(1)

where I is the Identity Matrix. Then the inverse of

is approximately

(2)

This can be seen by multiplying

Note that if we instead let , and look for an inverse of the form , we obtain


			(4)

In order to eliminate the

term, we require

. However, then

, so

so there can be no inverse of this form.

The exact inverse of can be found as follows.

(5)

(6)

Using a general Matrix Inverse identity then gives

(7)

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