Discussion Overview
The discussion revolves around the properties of the one and infinity norms of complex vectors, particularly in relation to their conjugate transposes. Participants explore why these norms are not equal for complex vectors, contrasting this with the behavior observed in the 2-norm.
Discussion Character
- Technical explanation, Conceptual clarification, Debate/contested
Main Points Raised
- One participant questions why the one and infinity norms of a complex vector x differ from those of its conjugate transpose x*.
- Another participant asks for clarification on the definition of the infinity norm of x*.
- A participant provides a definition of the infinity norm of x* as the maximum of the absolute values of the components of the conjugate transpose.
- There is a suggestion that the one and infinity norms may not be equal for complex vectors, but could be equal for real vectors.
- A participant discusses the absolute value of a complex number and its relationship to the norms, indicating a potential connection to the norms' properties.
Areas of Agreement / Disagreement
Participants express uncertainty regarding the equality of the norms for complex vectors, with some suggesting they may be equal for real vectors. The discussion does not reach a consensus on the implications of these properties.
Contextual Notes
Participants do not fully resolve the implications of their definitions and observations, leaving some assumptions and conditions unaddressed.