I need to invert the matrix $(I + \lambda B)^{-1}$ for several $\lambda$s. An identity of the form $(I + \lambda B)^{-1} = f(\lambda, B, B^{-1})$ would shortcut the costly matrix inversions. Any ideas?
Is there a matrix identity for $(I + \lambda B)^{-1}$, B full rank?
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linear-algebra
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3If the $\lambda$ are such that $\lVert\lambda B\rVert<1$ then you can use a series, namely $\sum_{k=0}^{+\infty}(-1)^k\lambda^k B^k$. – 2012-06-24
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0Would it be an option to use diagonalization of B? – 2012-07-25