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Unit 20: Cyclic Decomposition and the Rational Form

T-admissible Subspace: An invariant subspace W with another T-invariant subspace W , such that Notes
V = W W
is called T-admissible subspace.

20.6 Review Questions

3
1. Let T be the linear operator on R which is represented in the standard ordered basis by

3 4 4
1 3 3
2 4 3

Find non-zero , , satisfying the conditions of theorem 1.
1 2 3
2. Find the minimal polynomial and the rational forms of the following real matrices

0 1 1 C 0 1
1 0 0 , 0 C 1
1 0 0 1 1 C

Answer: Self Assessment

1. The characteristic polynomial is
f (x 1)(x 2) 2

The minimal polynomial is
p (x 1)(x 2)

20.7 Further Readings

Books Kenneth Hoffman and Ray Kunze, Linear Algebra
Michael Artin, Algebra

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