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

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Linear Algebra and Its Applications, Exercise 3.2.6

Exercise 3.2.6. Suppose that and are unit vectors. Then a one-line 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

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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

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