14. Suppose A is a real n x n matrix. a. What is the definition for A being positive definite? b. Suppose f:R” Ris smoot

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14 Suppose A Is A Real N X N Matrix A What Is The Definition For A Being Positive Definite B Suppose F R Ris Smoot 1 (49.32 KiB) Viewed 18 times

14. Suppose A is a real n x n matrix. a. What is the definition for A being positive definite? b. Suppose f:R” Ris smooth. What is the gradient of f? What significance does the gradient have? C. Suppose f: RM → R is smooth. What does it mean so say that u € Rº is a critical point of f? d. Suppose f:R” Ris smooth. What is f"(x). What special property does it have? e. Suppose f: RM → R is smooth, and u ER" is a critical point of f. Explain how to use determinants of principle minors of A = f'(u) to classify this critical point off as either a place where f has a local minimum or a local maximum. -