Ok, so I understand that a vector space is basically the span of a set of vectors (i.e.) all the possible linear combination vectors of the set of vectors...(adsbygoogle = window.adsbygoogle || []).push({});

I don't understand the concept behind a subspace or why it's useful.

I know the conditions are:

1. 0 vector must exist in the set

2. If you add two vectors in the set together, you should get another vector in the set

3. If you multiply a vector by a scalar, you should get another vector in the set.

Do conditions 2 and 3 combine? In other words, can the conditions be rewritten as

1. 0 vector must exist

2. A linear combination of some vectors gives another vector in the set

?

Also, graphically, what is the subset supposed to mean? It seems like the only way for something to be a subspace of Rn, for example, would be to be the vector space Rn...

Could someone give me an analogy to spark some intuition...because this seems very abstract?

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# Interpretation of a Subspace

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