MATH 415 Study Guide - Final Guide: Triangular Matrix, Qi, Mimo

• School: University of Illinois
• Department: Mathematics
• Course: MATH 415
• Professor: J Li

Document Summary

Application of qr and orthogonality, mimo and inner products. In the week of the 3rd exam (november 26-nov. 29th) the tutoring room will move to 1306 everitt hall: monday 4-8pm, tuesday 6-8pm, wednesday 4-8pm, thursday 4-6pm. Textbook reading: chapter 3. 4 subsection function spaces and fourier series. 1. 1: let a be an m n matrix of rank n. (columns independent) then a has a qr decomposition a = qr: Q is m n with orthonormal columns. R is n n, upper triangular and invertible: to obtain a = qr, use: q1 q2 a1 a2 qt. Gram-schmidt on (columns of) a, to get (columns of) q. Then r = qt a. (actually unnecessary!) Qr is a little slower than lu, but makes up in numerical stability. In multiple-input and multiple-output (mimo) systems, a transmitter sends multiple streams through multiple transmit antennas. Suppose there are n transmitters and m receivers. Then this is modeled by the matrix equation y1 ym.