Basis vector and Conical combination

Asked Jul 25 '17 at 18:02

Active Jul 25 '17 at 18:02

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I need your expertise in understanding the following:

Let $B = \{v_i\}_{i=1}^n$ be a basis vectors such that $\forall_{i \in [n]} v_i \in \mathbb{R}^n$ and let $w \in \mathbb{R}^n$. Its known that w can be represented as a linear combination of $B$ however what must be shown that $w$ is can also be represented as Conical combination of $B$?

Please advise and thanks in advance.

asked Jul 25 '17 at 18:02

user3492773

What is a conical combination? – Bernard Jul 25 '17 at 18:03
In linear combination, the coefficients that will be multiplied by the basis vectors can be any scalar while in conical combination these coefficients are non-negative scalars – user3492773 Jul 25 '17 at 18:17
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I don't think this is true without further conditions. The vector $-v_i$ is not going to be a conical combination. – A. Thomas Yerger Jul 25 '17 at 18:18
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What kind of conditions can we establish on $w$ such that we can ensure conical combination using $B$? – user3492773 Jul 25 '17 at 18:21

Basis vector and Conical combination

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