Tag Archives: arithmetic mean

Linear Algebra and Its Applications, Exercise 3.3.23

Posted on December 24, 2016 by hecker

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 →

Posted in linear algebra | Tagged , | Leave a comment

Linear Algebra and Its Applications, Exercise 3.2.6

Posted on May 10, 2014 by hecker

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 →

Posted in linear algebra | Tagged , , | Leave a comment

Linear Algebra and Its Applications, Exercise 3.2.1

Posted on April 20, 2014 by hecker

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 , , , | Leave a comment