SUMMARY
The distance of the ∞-norm between two vectors in ℝ³ is calculated by first subtracting the vectors and then applying the norm. Specifically, the formula used is ||u - v||, where u and v are the vectors in question. This method aligns with the definition of a normed distance in metric spaces, confirming that the correct approach is to find the difference before taking the maximum value of the absolute differences.
PREREQUISITES
- Understanding of vector operations in ℝ³
- Familiarity with the concept of norms in mathematics
- Knowledge of metric spaces and their properties
- Basic proficiency in mathematical notation and terminology
NEXT STEPS
- Study the properties of different norms, including the ∞-norm and its applications
- Learn about metric spaces and how distances are defined within them
- Explore vector subtraction and its implications in higher-dimensional spaces
- Investigate other types of norms, such as L1 and L2 norms, for comparative analysis
USEFUL FOR
Mathematicians, data scientists, and anyone working with vector spaces and distance calculations in multi-dimensional analysis.