No, the inverse of A-B is not a nice function of the inverses of A and B. (Of course it's possible to calculate -- if you have the inverses of A and B then you can calculate A and B, hence A-B, hence the inverse of A-B -- but, assuming you knew A and B anyway, knowing their inverses too doesn't help you calculate A-B more efficiently or accurately.)
There are some special cases where you can do something useful. For instance, if one of the matrices has rank 1 then this is basically the Sherman-Morrison formula. But in general you're out of luck.
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不，AB 的反函数不是 A 和 B 的反函数。（当然，计算是可能的——如果你有 A 和 B 的反函数，那么你就可以计算 A 和B，因此 AB，因此 AB 的逆 - 但是，假设您无论如何都知道 A 和 B，知道它们的逆也无法帮助您更有效或更准确地计算 AB。）
在某些特殊情况下，您可以做一些有用的事情。例如，如果其中一个矩阵的秩为 1，那么这基本上就是谢尔曼-莫里森公式。但总的来说，你运气不好。
No, the inverse of A-B is not a nice function of the inverses of A and B. (Of course it's possible to calculate -- if you have the inverses of A and B then you can calculate A and B, hence A-B, hence the inverse of A-B -- but, assuming you knew A and B anyway, knowing their inverses too doesn't help you calculate A-B more efficiently or accurately.)
There are some special cases where you can do something useful. For instance, if one of the matrices has rank 1 then this is basically the Sherman-Morrison formula. But in general you're out of luck.