Hello.
This is an exercise is from Hoffman, Linear Algebra, chapter7.4; but it has no solution, Can you help me to understand how tosolve it? I have just a very general idea of how to solve it and Iam afraid that, if the degree of the polynomial is changed, I mayfail the solution.
4. Construct a linear operator T with minimal polynomial x^2 (x- 1)^2 and characteristic
polynomial x^3(x-1)^4. Describe the primary decomposition of thevector
space under T and find the projections on the primary components.Find a basis
in which the matrix of T is in Jordan form. Also find an explicitdirect sum decomposition
of the space into T-cyclic subspaces as in Theorem 3 and give theinvariant
factors.
Best Regards.
