Cauchy Schwarz question
I have no idea to start. I'm struggling so much in this class. Can someone help me out?
(a) Given that x² + y² + z² = 1, use the cauchy-schwarz inequality to find the largest possible value of the expression 2x + 3y + 6z
(b) Let A be a diagonalizable matrix, all of whose eigenvalues are either 0 or 1. Show that A² = A
thanks in advance!
If A = (2,3,6) and B = (x,y,z), then
is the expression you want to maximize.
Cauchy Schwarz says
For the 2nd, try
since D has only diagonal elements 0 or 1.
(b)Since A is a diagonalizable matrix, there exist invertable matrix B and diagonal matrix D( whose diagonal elements are 0 or 1), such that
since , that is,
combined with B is invertable, gives the result.