Homework Help Overview
The discussion centers around the eigenvalues of the matrix product ATA, where A is an m x n matrix with rank m, indicating that m is less than n. The original poster explores the implications of this setup, particularly regarding the existence of eigenvalues and the specific case of zero being an eigenvalue.
Discussion Character
- Exploratory, Assumption checking, Conceptual clarification
Approaches and Questions Raised
- The original poster attempts to demonstrate that zero is an eigenvalue of ATA and questions what additional information can be derived about the eigenvalues of this matrix. Other participants introduce concepts related to the spectral theorem and its relevance to symmetric matrices, while also questioning the necessity of that theorem in this context.
Discussion Status
The discussion is active, with participants exploring different aspects of the eigenvalue problem. Some guidance has been provided regarding the implications of multiplying the eigenvalue equation by xT, and there is an ongoing exploration of the relationship between the properties of symmetric matrices and the eigenvalues of ATA.
Contextual Notes
Participants note that the spectral theorem was not covered in their course, which may limit the depth of discussion regarding the diagonalizability of the matrix in question. There is also a recognition of the constraints imposed by the course content on the exploration of eigenvalues.