Applied Mathematics 1411A/B Chapter Notes - Chapter 4.2.1: Scalar Multiplication

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It is often the case that some vector space of interest in contained within a larger vector space whose properties are known. In this section we will show how to recognize this and explain how the properties of the larger vector space can be used to obtain properties of the smaller vector space. A subset w of a vector space v is called a subspace of v if w is itself a vector space under the conditions discovered in section 4. 1 (addition and scalar multiplication defined on v). Well for the subspace vector space, there are some conditions that do not need to be verified as their verification is inherited from their verification in the parent vector space. So like, if condition 2 (u + v = v + u) is verified in v and w is a subspace of v, then this verification can be inherited by w and you don"t need to check it again.

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