MATH 415 Study Guide - Final Guide: Symmetric Matrix, Null Character, Row And Column Spaces

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

Document Summary

Suggested practice exercises: chapter 6. 3, # 1, 2, 3, 5, 8, 9, 15. If a is an n n symmetric matrix, then it has an orthonormal basis of eigenvectors v1 . vn, and all eigenvalues are real: we can write. A = v1 vn matrix of eigenvectors. {z: today: there is a similar decomposition for any m n matrix a. The price we pay: di erent bases on the left and right sides. Starting with an m n matrix a we want to: describe the geometry of the corresponding map rn rm, find a way to approximate a by simpler matrices, that are easier/cheaper to calculate with. How?remember: for each a we get 4 subspaces: input space rn contains row space col(at ) and null space nul(a). Di- mensions are r and n r: output space rm contains columns space col(a) and left null space.