Question

If a square matrix of order 100 has exactly 15 distinct eigen values, then the degree of the minimal polynomial is

• A. At least 15
• B. At most 15
• C. Always 15
• D. Exactly 100

Answer 1

The correct option is A At least 15

By property of "minimal polynomial" . If matrix has 15 distinct Eigen values, then its minimal polynomial must be of at least 15 degree.