幾題小問題

True or False (括弧內是給的答案)

(F)1.If x is an eigenvector of the matrix product AB, then Bx is an eigenvector of BA

x不等於0 , ABx=入x , => BABx=入Bx 哪裡不對呢?
(F)2.If a matrix U has orthonormal columns, then UU^T = I

(U^T)U=I => U^-1= (U^T) => UU^T= I 這又哪裡不對呢? 問題出在 orthonormal columns?
這和 orthonormal matrix有什麼不同呢?

(F)3.A least-squares solution of Ax = b is the vector Ax' in column space of A that is closest to b, so that b − Ax' <= b − Ax for all x.

這題也不大懂 least square solution (A^TA)^-1*A^T*b 跟 Ax' 有什麼關係.....



煩請解答了 謝謝