Project ForgeEngineering Mathematics
Linear Algebra
GATE 2007
Easy
If a square matrix A is real and symmetric, then the eigenvalues
- are always real
- Bare always real and positive
- Care always real and non-negative
- Doccur in complex conjugate pairs
Explanation
A standard spectral-theorem result: every real symmetric matrix has only real eigenvalues (they need not be positive or non-negative — that would additionally require positive/positive-semi-definiteness).
Source: GATE ME 2007 (2007)
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