MATH 415 Study Guide - Final Guide: Grayscale, Facial Recognition System, Asteroid Family

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

Document Summary

, um orthonormal eigenbasis of aat . v1, . , vn orthonormal eigen- basis for at a: can be rewritten in column times row form. We have a grayscale picture that is m n pixels in size: Each pixel is a shade of gray from 0 (black) to 255 (white). This gives an m n matrix a. Each entry of a is one pixel of the image; that entry is some integer from 0 to 255, giving the brightness of that pixel. Recall we can rewrite this as (with 1 2 3 . For most pictures r = 625, the maximal rank of a. Throw away the term ui ivt i when i is small. The matrix ak is very close to the matrix a, if k+1, . Ak is also easier to store: if k = 100, then to store the matrix a100 we need the numbers 1, .