Page 235 - DMTH502_LINEAR_ALGEBRA

Unit 21: The Jordan Form

21.5 Review Questions Notes

1. The differentiation operator on the space of the polynomials of degree less than or equal
to 3 is represented by the matrix

 0 1 0 0
 0 0 2 0 
 
 0 0 0 3
 
 0 0 0 0 
What is the Jordan form of the matrix?
2. If A is a complex 5 × 5 matrix with the characteristic polynomial
3
f = (x – 2) (x + 7) 2
2
and the minimal polynomial p = (x – 2) (x + 7), what is the Jordan form for A?
Answer: Self Assessment

1. Trace of A = c d + c d + ... + c d
1 1 2 2 k k
21.6 Further Readings

Books Kenneth Hoffman and Ray Kunze, Linear Algebra
I.N. Herstein, Topics in Algebra

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