Homework Statement
Prove that if A: V - >V is a linear map, dim V = n, and h1,...,hk (where 1,...,k are subscripts) are pairwise different eigenvalues of A such that their geometric multiplicities sum to n, then A does not have any other eigenvalues.
Homework Equations
Note sure if this is...
Homework Statement
Let V be the vector space of all real-coefficient polynomials with degree strictly less than five. Find the eigenvalues and their geometric multiplicities for the following maps from V to V:
a) G(f) = xD(f), where f is an element of V and D is the differentiation map...
Homework Statement
Find the number of elements in the ring Z_5[x]/I, where I is a) the ideal generated by x^4+4, and b) where I is the ideal generated by x^4+4 and x^2+3x+1.
Homework Equations
Can't think of any.
The Attempt at a Solution
I started by finding the zeros of the...