LECTURES IN BASIC COMPUTATIONAL NUMERICAL ANALYSIS
In the case of Euclidean spaces, we can define another useful object related to the Euclidean norm, the inner product (often called the “dot product” when applied to finite-dimensional vectors). Definition 1.3 Let S be a N-dimensional Euclidean space with v,w ∈ S. Then hv,wi ≡ XN i=1 viwi (1.4) is called the inner product.
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web.engr.uky.edu1.1. SOME BASIC FACTS FROM LINEAR ALGEBRA 3 Theorem 1.1 (Cauchy–Schwarz) Let S be an inner-product space with inner product h· ,·i and norm k· k2. If v,w ∈ S, then hv,wi ≤ kvk2 kwk2. (1.5) We have thus far introduced the 2-norm, the infinity norm and the inner product for spaces of finite-dimensional vectors.
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