A function f(x) on Rn is called homogeneous of degree k if f(cx) = ci(x) for all

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A function f(x) on Rn is called homogeneous of degree k if f(cx) = ci(x) for all scalars c.
(a) If a ˆˆ Rn is a fixed vector, show that a linear form £(x) = a . x = a1X1 +-----+ anxn is homogeneous of degree 1.
(b) Show that a quadratic form

is homogeneous of degree 2.
(c) Find a homogeneous function of degree 2 on R2 that is not a quadratic form.

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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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Question Posted: Jun 17, 2016 08:40 AM

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A function f(x) on Rn is called homogeneous of degree k if f(cx) = ci(x) for all

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a cx a cx c a x c x b qcx cx ...View the full answer

Applied Linear Algebra

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