Inner Products in R2 other than euclidian

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SUMMARY

The discussion centers on the properties of inner products in R², specifically focusing on the requirements for an inner product to be symmetric, linear, and positive definite. Participants emphasize the necessity of demonstrating linearity in inner products and the specific form of the dot product. The conversation highlights the mathematical rigor needed to establish these properties in vector spaces.

PREREQUISITES
  • Understanding of vector spaces and their properties
  • Familiarity with the definition of inner products
  • Knowledge of linear algebra concepts, particularly linearity
  • Basic comprehension of symmetric and positive definite matrices
NEXT STEPS
  • Study the proof of linearity in inner products
  • Explore the properties of symmetric matrices in linear algebra
  • Investigate positive definite forms and their applications
  • Learn about alternative inner products in R² beyond the standard dot product
USEFUL FOR

Mathematicians, students of linear algebra, and anyone interested in advanced vector space concepts will benefit from this discussion.

corey2014
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Hint: An inner product for a real vector space has to be symmetric, linear, and positive definition.
 
Yes, i know the definition, however i don't know how to show that it has to be linear, or that the dot product has to be of that form...
 

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