1. Let A[itex]\in[/itex]Rnxn be a symmetric matrix, and assume that there exists a matrix B[itex]\in[/itex]Rmxn such that A=BTB. a) Show that A is positive semidefinite B) Show that if B has full rank, then A is positive definite 2. Relevant equations: This is for an operations research class, so most of the definitions revolve around minimizing/maximizing. However, alternate definitions: Positive Definite: A is positive definite if for all non-null vectors h, hTAh > 0. Symmetric: if AT=A. Semidefinite: hTAh ≥ 0 3. The attempt at a solution Here's some work: AT = A ; A = BTB. So, AT = BTB → ATA = BTBA = AA = A2. So, ATA ≥ 0. But, that's not quite what I want.