In Exercise 13, the Frobenius norm of a matrix was defined. Show that for any n x n matrix A and vector x in M", ||Ax||2 < II A||/r||x||2.

Spencer Kociba MATH 200005 Lecture Notes Week 2 09/26/2016 Dot Products and Projections ● Dot product ○ Notation of vector a dotted with vector b= a∙b ○ [a❑ ,1❑ ..2a❑ ∙ bn][b❑ .1.b❑ 2a❑ b❑ n]❑ b❑ 1...1a❑ b❑ 2 2 n n ■ Answer=a scalar value. NOT a vector ■ ^^^vectors of size n dimensions can be represented by a matrix of 1xn size or nx1 size ■ Ex. [25]∙[71]=(2)(7)+(5)(1)=14+5=19 ○ Can be used to find length ■ Ex. If aisthevector[a❑ ,1❑ ..2a❑ n]