Homework Help Overview
The discussion revolves around the concept of eigenvectors and their role in forming a basis for vector spaces in quantum mechanics, particularly in the context of linear transformations. The original poster questions the assertion that eigenvectors can always form a basis if they span the space, suggesting that fewer than n vectors might suffice.
Discussion Character
- Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants explore the relationship between the number of eigenvectors and the dimensionality of the vector space, questioning whether all eigenvectors are necessary to form a basis. The original poster raises concerns about the completeness of eigenvectors in spanning the space.
Discussion Status
The conversation is ongoing, with participants providing insights into the conditions under which eigenvectors can form a basis. There is recognition of the possibility that not all eigenvectors may be linearly independent, which could affect their ability to span the space.
Contextual Notes
There is an underlying assumption that the linear operator in question may not always have n linearly independent eigenvectors, which is central to the discussion about the nature of eigenbases.