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Tag Archives: arithmetic mean
Linear Algebra and Its Applications, Exercise 3.3.23
Exercise 3.3.23. Given measurements show that the best least squares fit to the horizontal line is given by Answer: This corresponds to the system where is an by 1 matrix with all entries equal to 1 and . To find the … Continue reading
Linear Algebra and Its Applications, Exercise 3.2.6
Exercise 3.2.6. Suppose that and are unit vectors. Then a oneline proof of the Schwarz inequality is as follows: What previous exercise justifies the middle step of this proof? Answer: From exercise 3.2.1(a) we have for any positive and . … Continue reading
Linear Algebra and Its Applications, Exercise 3.2.1
Exercise 3.2.1. a) Consider the vectors and where and are arbitrary positive real numbers. Use the Schwarz inequality involving and to derive a relationship between the arithmetic mean and the geometric mean . b) Consider a vector from the origin … Continue reading
Posted in linear algebra
Tagged arithmetic mean, geometric mean, Schwarz Inequality, triangle inequality
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