Project ForgeEngineering Mathematics
Linear Algebra
GATE 2013
Easy
The eigenvalues of a symmetric matrix are all
- Acomplex with non-zero positive imaginary part.
- Bcomplex with non-zero negative imaginary part.
- real.
- Dpure imaginary.
Explanation
A fundamental theorem of linear algebra: every real symmetric matrix has only real eigenvalues (and its eigenvectors can always be chosen orthogonal). This follows from A=Aᵀ making the Rayleigh quotient real for any eigenvector.
Source: GATE ME 2013 (Booklet Code A) (2013)
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