# Questions tagged [inverse]

Inverses include: multiplicative inverse of a number (reciprocal), inverse function, matrix inverse, etc. A subject tag such as (linear-algebra), (algebra-precalculus) or (arithmetic) should be added to clarify in which sense "inverse" is used. This tag should never be the only tag on a question.

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### Invertibility (and eigen-decomposition) of complex symmetric matrix?

Consider $Z = K - i \omega S - \omega^2 M$, where: $\omega$ is a positive real number; $K$ is a real, symmetric, and positive semi-definite matrix; $M$ is a real, symmetric, and positive definite ...
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### Is there always a smooth variant of a homeomorphism between smooth manifolds?

Let $M$ and $N$ be smooth homeomorphic manifolds. Let $h:M\rightarrow N$ a homeomorphism. Does there exist $r:M\rightarrow N$ that is still a homeomorphism and additionaly smooth? Can it be chosen ...
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### Is the inverse of any elementary function asymptotic to some elementary function?

Is the functional inverse of any elementary function asymptotic to some elementary function ? For instance Lambert's $W(z)$ is asymptotic to $ln(z)$. See http://mathworld.wolfram.com/LambertW-Function....
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### SVD of matrix plus diagonal matrix and inversed

Assume we have a matrix $Z$ and we know its singular value decomposition. So, based on this, is there any trick for computing SVD of $(Z+cI)^{-1}$, where $cI$ is identity matrix, multiplied by some ...
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### Under what circumstances can we take this inverse matrix?

Assume we have a matrix: $$(A^TB^{-1}A)^{-1}.$$ Under what circumstances can we simplify this to: $$C^TBC?$$ And what would $C$ be? EDIT: Note that I am NOT assuming that $A$ is a square ...
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