110年 - 110 國立中山大學碩士暨碩士專班招生考試_應數系碩士班/丙組:線性代數丙#104308

1. [10%] Let be a linearly independent sct in some vector space over C. Find all value(s) of forms a linearly independent set.

(4) Let be a linearly independent subsct of S. What is the possible maxinal value of n?

3. [15%] Let T be the linear transform on the sct M_n(R) of n X n matrices over R defined as T(A) = (A+ A^t)/2, where A^t stands for the transpose of . Find all eigenvalues of

4. [15%] Find the Jordan form of the matrix
  

5. [15%] Let T : R³ → R³ be linear so that its matrix representation under some basis of R³is

Show that there is no trivial invariant subspace for T.

6. [15%] Let T:V →V be a lincar map, where Y is a vector space with dimension nh. Suppose that there exists some voe rctor Show that with respect to some basis of V, T has the matrix reprosentation of the form