
(Sperner's lemma in dimension 3) (a) *Consider a tetrahedron T- A1A2A3A4 in the 3-dimensional space and some subdivision of T into small tetrahedra, such that each face of each small tetrahedron...
Mostly need help with part b:
(a) * Consider a tetrahedron T = A1 A2A3A4 in the 3-dimensional space and some subdivision of T into small tetrahedra, such that each face of each small tetrahedron either lies on a face of the big tetrahedron or is also a face of another small tetrahedron. Let us label the vertices of the small tetrahedra by labels 1. 2, 3, 4, in such a way that the vertex Ai gets i, the edge...
8. Suppose V is an n-dimensional complex vector space. Suppose T E C(V) is such that 1,2, and 3 are the only distinct eigenvalues of T (a) Prove that the dimension of each generalized eigenspace of T is at most (n - 2). (b) Show that (T-1)"-2(T-21)"-"(7-31)"-"(a) = 0V, for all α є V.
8. Suppose V is an n-dimensional complex vector space. Suppose T E C(V) is such that 1,2, and 3 are the only distinct eigenvalues of T...