251 Lecture 4 SVD - AMCS 251 A mathematician is a blind man...

Info icon This preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Click to edit Master subtitle style 4/14/11 AMCS 251 A mathematician is a blind man in a dark room looking for a black cat which isn't there. Charles Darwin
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Click to edit Master subtitle style 4/14/11 Lecture 3 - Reprise Induced norm What can you say about it?
Image of page 2
Click to edit Master subtitle style 4/14/11 Lecture 3 - Reprise Induced norm is smallest C so that for all x ||Ax|| = C||x|| ° D ||Ax|| / ||x|| = C
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Click to edit Master subtitle style 4/14/11 Lecture 3 - Reprise Induced norm is smallest C so that for all x ||Ax|| = C||x|| ° D ||Ax|| / ||x|| = C Makes the action of A independent of what ||x|| is
Image of page 4
Click to edit Master subtitle style 4/14/11 Lecture 3 - Reprise Induced norm is smallest C so that for all x ||Ax|| = C||x|| ° D ||Ax|| / ||x|| = C Makes the action of A independent of what ||x|| is Scale x by α ||Aαx|| / ||αx|| = |α|||Ax|| / |α|||x|| = ||Ax|| / ||x||
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Click to edit Master subtitle style 4/14/11 Lecture 3 - Reprise Induced norm is smallest C so that for all x ||Ax|| = C||x|| ° D ||Ax|| / ||x|| = C Makes the action of A independent of what ||x|| is Scale x by α ||Aαx|| / ||αx|| = |α|||Ax|| / |α|||x|| = ||Ax|| / ||x|| In other words, the induced norm Sup ||Ax|| / ||x|| for all ||x|| = 1 i.e. the unit sphere.
Image of page 6
Click to edit Master subtitle style 4/14/11 Lecture 4 - SVD Gauss vs Singular Value Decomposition?
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
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