0
$\begingroup$

when we are checking whether a subset v is a subspace or not , we search for two main things :

  1. closed under addition
  2. closed under scalar multiplication

my 2 question are

does scalar multiplication include zero ?

does addition include the additive inverse?

as if it does then any subset that doesn't include the zero matrix won't be considered a subset

$\endgroup$
2
  • $\begingroup$ "When we are checking whether a subset v is a subset or not"... a subset is always a subset. The question is usually in this context whether it is a subspace or not. "...any subset that doesn't include the zero vector won't be considered a subspace" $\endgroup$
    – JMoravitz
    Commented Oct 1, 2019 at 18:08
  • $\begingroup$ subspace thing was a typo(fixed it ) . thanks for your answer $\endgroup$ Commented Oct 1, 2019 at 18:42

1 Answer 1

0
$\begingroup$

The answer to both questions is affirmative. And, yes, it follows from this that, if a subset $S$ of a vector space is such that $0\notin S$, then $S$ is not a subspace.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .