Some standard results of matrix theory are derived in a manner designed to appeal to physicists and are illustrated by examples from quantum mechanics. Sylvester's formulas, expressing a function of any n-dimensional square matrix as a linear combination of the first n−1 powers of A, are applied to the evaluation of the rotation matrices D(i)(R) for low values of j. The neutral K meson is used as an example of the usefulness of matrix techniques for systems with two basis states.

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