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9: Inner product spaces

  • Page ID
    257
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    The abstract definition of a vector space only takes into account algebraic properties for the addition and scalar multiplication of vectors. For vectors in \(\mathbb{R}^n\), for example, we also have geometric intuition involving the length of a vector or the angle formed by two vectors. In this chapter we discuss inner product spaces, which are vector spaces with an inner product defined upon them. Inner products are what allow us to abstract notions such as the length of a vector. We will also abstract the concept of angle via a condition called orthogonality.


    This page titled 9: Inner product spaces is shared under a not declared license and was authored, remixed, and/or curated by Isaiah Lankham, Bruno Nachtergaele, & Anne Schilling.

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