This monograph proposes that viewing the resolvent of a matrix as a meromorphic function rather than just analytic outside the eigenvalues provides new insight, and develops a new non-linear tool for linear algebra the total logarithmic size of a matrix which allows the author to generalization his uncle's first main theorem from the scalar valued case for matrix valued functions. The author then proves the robustness of the growth of the resolvent as a meromorphic function under low rank perturbations, and studies the growth of a meromorphic function by approximating rational functions. Annotation (c) Book News, Inc., Portland, OR (booknews.com)

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