For ๐ > 1, the maximum multiplicity of any eigenvalue of an ๐ร๐ matrix withโฆ
2026
For ๐ > 1, the maximum multiplicity of any eigenvalue of an ๐ร๐ matrix with elements from โ is
Answer: A. n โ The multiplicity of an eigenvalue refers to its algebraic multiplicity, i.e., the number of times it appears as a root of the characteristic polynomial. Forโฆ
- A.
n
- B.
n-1
- C.
1
- D.
n+1
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Correct answer: A
The multiplicity of an eigenvalue refers to its algebraic multiplicity, i.e., the number of times it appears as a root of the characteristic polynomial.
For an nรn matrix:
The characteristic polynomial has degree n.
Therefore, the sum of the algebraic multiplicities of all eigenvalues is exactly n.
Hence, the maximum possible multiplicity of a single eigenvalue is n.
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