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.
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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. ∙=(2)(7)+(5)(1)=14+5=19 ○ Can be used to find length ■ Ex. If aisthevector[a❑ ,1❑ ..2a❑ n]
Textbook: Numerical Analysis
Author: Richard L. Burden J. Douglas Faires, Annette M. Burden
Numerical Analysis was written by and is associated to the ISBN: 9781305253667. This textbook survival guide was created for the textbook: Numerical Analysis, edition: 10. This full solution covers the following key subjects: . This expansive textbook survival guide covers 76 chapters, and 1204 solutions. The full step-by-step solution to problem: 14 from chapter: 7.1 was answered by , our top Math solution expert on 03/16/18, 03:24PM. The answer to “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.” is broken down into a number of easy to follow steps, and 29 words. Since the solution to 14 from 7.1 chapter was answered, more than 232 students have viewed the full step-by-step answer.