Tag Archives: inner product

Linear Algebra and Its Applications, Exercise 3.4.20

Posted on January 2, 2018 by hecker

Exercise 3.4.20. Given the vector what is the length ? Given the function for what is the length of the function over the interval? Given the function for what is the inner product of and ? Answer: We have so … Continue reading →

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Linear Algebra and Its Applications, Exercise 3.2.16

Posted on June 15, 2014 by hecker

Exercise 3.2.16. a) Given the projection matrix projecting vectors onto the line through and two vectors  and , show that the inner products of with and with are equal. b) In general would the angles between and and and be … Continue reading →

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Commutative and distributive properties for vector inner products

Posted on April 19, 2014 by hecker

As I think I’ve previously mentioned, one of the minor problems with Gilbert Strang’s book Linear Algebra and Its Applications, Third Edition, is that frequently Strang will gloss over things that in a more rigorous treatment really should be explicitly … Continue reading →

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Linear Algebra and Its Applications, Exercise 3.1.1

Posted on February 1, 2014 by hecker

Exercise 3.1.1. For and what is the length of each vector and their inner product? Answer: We have and so that and . The inner product of and is then Note that and are thus orthogonal. NOTE: This continues a … Continue reading →

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Linear Algebra and Its Applications, Review Exercise 2.31

Posted on January 18, 2014 by hecker

Review exercise 2.31. Consider the rank-one matrix . Under what conditions would ? Answer: In order for to exist must be a square matrix; otherwise we could not multiply by since the number of columns of the first matrix would … Continue reading →

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