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Calculus: Concepts and Methods by Joan Davies, Ken Binmore

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Six

Optimisation of scalar valued functions

The technique in classifying the stationary points of a real valued function of one real variable is to examine the sign of the second derivative. The same technique works in the case of a real valued function of a vector variable except that, in this case, the second derivative is a matrix. Instead of asking whether this second derivative is positive or negative we ask instead whether it is ‘positive definite’ or ‘negative definite’. The chapter begins with a section on linear algebra which explains these notions, although it is possible for most purposes to manage just by remembering statements (I) ...

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