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- #1

Prove the converse.

We are working with finite dimensional vector spaces.

Let $\mathbf{v}(t) = \sum\limits_{i = 1}^{n}c_iv(t)_i$.

Then

$$

\lVert\mathbf{v}(t)\rVert = \sqrt{\sum\limits_{i = 1}^{n}c_i^2} = \alpha\in\mathbb{C}.

$$

How do I defined $\dot{\mathbf{v}}(t)$?