Question

Let $\mathbf{v} \neq \mathbf{0}$ be any nonzero vector in a normed vector space $V$. Show how to construct a new norm on $V$ that changes $\mathbf{v}$ into a unit vector.

    Let $\mathbf{v} \neq \mathbf{0}$ be any nonzero vector in a normed vector space $V$. Show how to construct a new norm on $V$ that changes $\mathbf{v}$ into a unit vector.

Applied Linear Algebra (Undergraduate Texts in Mathematics)

Applied Linear Algebra (Undergraduate Texts in Mathematics)

Peter J. Olver,… 2nd Edition

Chapter 3, Problem 26

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Since $\mathbf{v} \neq \mathbf{0}$, we have $\|\mathbf{v}\| > 0$. Show more…

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Let $\mathbf{v} \neq \mathbf{0}$ be any nonzero vector in a normed vector space $V$. Show how to construct a new norm on $V$ that changes $\mathbf{v}$ into a unit vector.

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