Ehm, this is kind of a dumb question (as in, it should be very easy and I'm just having a moment of confusion). If I'm given a linear transformation T from vector space V to vector space W (fininte dim) and I want to compute T-inverse, I know that I can compute the matrix representation of T and invert it. So my question is, once I have inverted the matrix, how do I reconstruct an explicit formula for T-inverse? I know the values of T-inverse on my basis (the coefficients) but it seems that this doesn't quite tell me what formula to use since more than one possibility exists.(adsbygoogle = window.adsbygoogle || []).push({});

Also, is there a good way to compute T-inverse without the use of the matrix representation? The only way I know how is if the mapping is from R to R, because that's like single variable calculus, but as soon as we have some other space I'm clueless without a matrix rep.

Ideas? Know what I mean? :shy:

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# Determing formula for T inverse

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