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gamerninja213
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Homework Statement
If the only eigenvalue is zero, can you ever get a set of n linearly independent vectors?
Is it possible to have a diagonal matrix with all eigenvalues = zero ?
- Thread starter gamerninja213
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Homework Help Overview
The discussion revolves around the properties of diagonal matrices and their eigenvalues, specifically focusing on whether a diagonal matrix can have all eigenvalues equal to zero and the implications for linear independence of vectors.
Discussion Character
- Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants explore the relationship between eigenvalues and linear independence, questioning whether a matrix with an eigenvalue of zero can still have linearly independent vectors.
Discussion Status
Some participants have provided insights into the nature of the zero matrix and its eigenvalues, while others have clarified the original question's intent. There is an ongoing exploration of the implications of having zero eigenvalues on the independence of vectors.
Contextual Notes
There appears to be a typo in the original question, which has led to some confusion regarding the intended inquiry about eigenvalues and linear independence.