MATH 415 Study Guide - Final Guide: Khan Academy, Qr Decomposition, Orthogonal Matrix

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

Document Summary

Suggested practice exercises: 3. 4: 13, 16, 17, 18. , vm is an orthonormal basis of w . The orthogonal pro- jection of x onto w is : xw = hx, v1iv1 proj. of x onto v1. + hx, vmivm proj. of x onto vm (to stay agile, we are writing hx, v1i = x v1 for the inner product. ) * in calculating projections we used an orthogonal basis and the easy formula for the coe cients. * turn the starting basis into an orthogonal (or orthonormal) basis. Find an orthonormal basis for v = span{ . 0 q1 = b1 b1 = a1, kb1k q2 = b2 b2 = a2 ha2, q1iq1, kb2k b3 = a3 ha3, q1iq1 ha3, q2iq2, q3 = b3 kb3k q1 = q2 = . We have obtained an orthonormal basis for v : q1, q2, q3. b1 = b2 = b3 = . Recall, if w is a subspace, b any vector, then.