Practice question · Sort into groups
Classify each matrix property in terms of its eigenvalues.
Groups: Related to eigenvalues · Not directly related
- Invertibility (no zero eigenvalue)
- Trace = sum of eigenvalues
- Matrix is symmetric
- Number of rows
- Determinant = product of eigenvalues
Hints
- Each property corresponds to a sum, a product, or a zero among the roots.
- Invertibility fails exactly when one root vanishes.
Show the answer
Related to eigenvalues: Trace = sum of eigenvalues, Determinant = product of eigenvalues, Invertibility (no zero eigenvalue)
Not directly related: Number of rows, Matrix is symmetric
Why
Trace, determinant, and invertibility are all characterised by eigenvalues.
Practise Eigenvalues and Eigenvectors
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