GATE EE 2014 Set 2 — Question 11

MCQ+1 / -0.33EasyEigenvalues & EigenvectorsLinear AlgebraEngineering Mathematics

Engineering Mathematics → Linear Algebra → Eigenvalues & Eigenvectors

Last updated 5 September 2026

Question

Which one of the following statements is true for all real symmetric matrices?

Correct answer (A) All the eigenvalues are real. Solution A fundamental property of real symmetric matrices is that all their eigenvalues are real. They are not necessarily positive (could be zero or negative), not necessarily distinct (can have repeated eigenvalues), and their sum is the trace of the matrix, which is not necessarily zero. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (A) All the eigenvalues are real. Solution A fundamental property of real symmetric matrices is that all their eigenvalues are real. They are not necessarily positive (could be zero or negative), not necessarily distinct (can have repeated eigenvalues), and their sum is the trace of the matrix, which is not necessarily zero.

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