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Tag Archives: inner product
Linear Algebra and Its Applications, Exercise 3.4.20
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
Linear Algebra and Its Applications, Exercise 3.2.16
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
Commutative and distributive properties for vector inner products
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
Posted in linear algebra
Tagged commutative property, distributive property, inner product
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Linear Algebra and Its Applications, Exercise 3.1.1
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
Linear Algebra and Its Applications, Review Exercise 2.31
Review exercise 2.31. Consider the rankone 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