Inner Products and Inner Product Spaces | Linear Algebra

We introduce inner products and inner product spaces. We'll see how the inner product axioms come directly from the basic properties of the dot product, we'll briefly discuss complex inner product spaces and the symmetry axiom for such spaces, we'll see how norms and distances are defined and calculated in inner product spaces, see examples and non-examples of inner product spaces including an inner product space of matrices, and will see basic algebraic properties of inner products. #linearalgebra

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0:00 Intro
1:29 Definition of Inner Product and Inner Product Space
4:26 Euclidean n-Space (with Dot Product)
4:58 Norm and Distance in Inner Product Space
5:45 Properties of Norm and Distance
6:31 Inner Product Non-Example
8:23 Weighted Euclidean Inner Product
11:59 Norm and Distance in Weighted Euclidean Inner Product Space
14:24 Algebraic Properties of Inner Products
17:42 Standard Inner Product on Square Matrices
20:08 Conclusion

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