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A matrix is positive definite fxTAx > Ofor all vectors x 0. Frequently in physics the energy of a system in state x is represented as XTAX (or XTAx) and so this is frequently called the energy

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A matrix is positive definite if it’s symmetric and all its pivots are positive. where Ak is the upper left k x k submatrix. All the pivots will be pos itive if and only if det (Ak) > 0 for

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