Vector and Inner Product Spaces

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Chapter 3 Vector and Inner Product Spaces

This chapter explores linear systems in a more abstract manner. We will see that framing vector and matrix addition and scalar multiplication in a more general way will allow us to make connections between seemingly disparate parts of mathematics and then discover new things because of this.

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We first investigate vector spaces, which at first seem like they are just sets of vectors, but are actually much more. Then we will see inner product spaces, another way of looking at vectors and finally linear transformations.

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