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If I have an object (is it correct to call it a tensor?) whose components are defined by:

[tex]X_{mikl}=(R^{-1})_{mi}R_{kl}-(S^{-1})_{mi}S_{kl},[/tex]

where R and S are invertible matrices. I want to find the "inverse" of X, i.e. to find (X^{-1}) such that,

[tex](X^{-1})_{qkpm}X_{mikl}=\delta_{lq}\delta_{pi}[/tex].

Is there a way to find out whether (X^{-1}) exists? A matrix doesn't have an inverse if its determinant is zero - is there a similar rule here? I've tried some trial functions for X^{-1} but nothing works, and I want to know whether there's a better way of tackling this problem.

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# Inverting a tensor?

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