{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

31_hwc1SolnsODDA - Therefore the angle n between these...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Therefore, the angle α n between these vectors is α n = 1 - ( rs ) n 1 - rs 1 - r 2 n 1 - r 2 - 1 / 2 1 - s 2 n 1 - s 2 - 1 / 2 = (1 - r 2 ) 1 / 2 (1 - s 2 ) 1 / 2 1 - rs 1 - ( rs ) n (1 - r 2 n ) 1 / 2 (1 - s 2 n ) 1 / 2 . (c) Since both | r | < 1 and | s | < 1, we have that lim n →∞ r 2 n = 0, lim n →∞ s 2 n = 0 and also, lim n →∞ ( rs ) n = 0. Therefore lim n →∞ n = 1 1 - r 2 and lim n →∞ α n = 1 - r 2 1 - s 2 1 - rs . You just computed the angle between two infinite dimensional vectors! This will turn out to be more than a mere curiosity. 4.7 Consider the vectors a = a b . Find all vectors c d that are orthogonal to a . That is find conditions on c and d in terms of a and b that are necessary and sufficient for this orthogonality. SOLUTION Computing the dot product, a b · c d = ac + bd . Thus, the vectors are orthogonal if and only if
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern