My Math Forum Symmetric matrix acting on a unit sphere

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 February 7th, 2013, 05:53 PM #1 Newbie   Joined: Feb 2013 Posts: 1 Thanks: 0 Symmetric matrix acting on a unit sphere If you take all vectors on a unit sphere in n dimensions and then transform them using a nxn symmetric matrix, then the maximum of the norms of the resulting vectors is equal to the maximum eigen value for the matrix... Can someone explain why this is for me or point me towards something that will. Thank you we know the formula ||Ax||/||x|| but not how it is derived or really what its for.
 February 17th, 2013, 06:54 AM #2 Newbie   Joined: Feb 2012 Posts: 28 Thanks: 0 Re: Symmetric matrix acting on a unit sphere It's been a while since I studied linear algebra but I remember that symmetric matrices are often used in the study of quadratic forms (which can be factored into, if I remember correctly, the matrices product $P D P^{-1}$. I may be wrong but it's definitely worth investigating quadratic forms if you're using symmetric matrices.

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