If V is diagonal, it is easy to show:(adsbygoogle = window.adsbygoogle || []).push({});

[itex](V + V^{-1})^{-1} = V(V^2 + I)^{-1}[/itex]

by multiplying both sides by:

[itex](V + V^{-1})[/itex]

But, I'm wondering if there is a way to derive the RHS from the LHS. Since diagonal matrices behave like scalars, I used a scalar analogy:

[itex] (x + 1/x)^{-1} = ((x^2 + 1)/x)^{-1} = x(x^2 + 1)^{-1}[/itex]

But I'd like to show it using matrix terminology. If there is something simple, I'm missing it. Any ideas?

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# Matrix Identify involving Diagonal Matrix

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