Discussion Overview
The discussion revolves around the behavior of the product Av^j in the context of Singular Value Decomposition (SVD) when the index j exceeds the rank r of the matrix A. Participants are exploring the implications of this scenario, particularly for values of j greater than r.
Discussion Character
- Exploratory, Technical explanation, Debate/contested
Main Points Raised
- One participant states that for 1 <= j <= r, Av^j equals sigma^j * u^j.
- The same participant questions what Av^j becomes for r + 1 <= j <= n, indicating a gap in understanding for this range.
- Other participants express uncertainty about the topic, with some indicating they do not have a clear idea or solution.
Areas of Agreement / Disagreement
There is no consensus among participants, as several express uncertainty and lack of knowledge regarding the behavior of Av^j for j greater than r.
Contextual Notes
The discussion lacks detailed exploration of the mathematical properties or definitions that might clarify the behavior of Av^j for j > r, leaving assumptions and implications unresolved.