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What is a vector space and vector subspace?

I’ve looked through so many websites and my textbook but I still cannot understand it.

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Answer #1

dear janice,you can’t answer a question like that in a few words ,however it is a mathematical structure, if you want more details contact me

Answer #2

A concept related to a space vectorial is that of a subespacio vectorial. We suppose that is a space vectorial and be a subset. This signifies that is composed of some (but not necessarily all) of the vectors in. As we saw previously with the example of the upper half of the airplane, not every subset will be in itself a space vectorial. It given that is a space vectorial, we know that we can add vectors and they multiply for escalares, but only in a space vectorial in itself if the results of these operations are back in. Formally, we have

Definition 1,11. A subset of a space vectorial is a subespacio vectorial of if the following two axioms are satisfied

If S1 and are vectors in, then is also it, and S2 For any to scale, if is any vector in, then is also it. Also it is utilized often the “phrases” is a subespacio of ‘and’ is a subespacio lineal of ‘.’

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