MATH 310 Study Guide - Midterm Guide: Triangular Matrix, Linear Map, Orthogonal Complement
Document Summary
Throughout this exam, v is a complex vector spaces of nite dimension endowed with an inner product h , i. The vector space of all com- plex polynomials is denoted by p; the subspace consisting of those polyno- mials of degree at most n is denoted by pn. {p (x) p|p ( 1) + p (2) = 0} is a subspace of p. {p (x) p|p (0) = 1} is a subspace of p. 0 p (t)dt = 0} is a subspace of p. If v cn is such that v + w v for all v, w v , then v is a subspace. Consider cn as a complex vectorspace; rn is a subspace. The union of two subspaces u1, u2 of v is a subspace if and only if either u1 u2 or u2 u2. The intersection of three subspaces of v is a subspace.
