251 Lecture 4 SVD

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

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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

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Click to edit Master subtitle style 4/14/11 Lecture 3 - Reprise Induced norm What can you say about it?
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

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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
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||

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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.
Click to edit Master subtitle style 4/14/11 Lecture 4 - SVD Gauss vs Singular Value Decomposition?

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