Discussion Overview
The discussion revolves around the notation used for representing the norm of vectors, specifically the use of double vertical lines (||w||) compared to single vertical lines (|w|). Participants explore the implications, origins, and conventions of this notation within the context of mathematical representation of vector magnitudes.
Discussion Character
- Conceptual clarification, Debate/contested
Main Points Raised
- Some participants note that the symbol || \cdot || is commonly used to represent the norm function on vectors.
- Others suggest that there is no profound logic behind the choice of double lines, viewing it as a chosen symbol.
- It is mentioned that single lines are also used for absolute values and determinants, and that the notation may have originated from these uses.
- One participant argues that while ||\text{whatever}|| is a well-agreed upon symbol for the Euclidean norm, there are infinitely many ways to define the length of a vector, all of which are norms.
- Another participant emphasizes that the notation ||w|| specifically denotes the magnitude of a vector, likening it to the absolute value of a number.
Areas of Agreement / Disagreement
Participants express differing views on the significance and origins of the notation, indicating that there is no consensus on whether the double lines have a deeper meaning or are simply a matter of convention.
Contextual Notes
Some limitations include the potential confusion between the notation for vector magnitudes and absolute values, as well as the varying definitions of norms that may not be universally agreed upon.