Let f(u) = u™ Au, where u e Rd and A e Rd×d is a symmetric matrix. Calculate Vuf(u).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 29E
icon
Related questions
icon
Concept explainers
Topic Video
Question

I need help on the last question of the three. 

• Let f(u) = aTu = E-1 a;U; for a, u E Rd. Calculate Vuf (u).
• Let f(u) = ||u||3 = E÷1 u? for u E Rd. Calculate Vuf(u).
• Let f(u) = uT Au, where u E Rd and A E Rdxd is a symmetric matrix. Calculate Vuf (u).
и
Transcribed Image Text:• Let f(u) = aTu = E-1 a;U; for a, u E Rd. Calculate Vuf (u). • Let f(u) = ||u||3 = E÷1 u? for u E Rd. Calculate Vuf(u). • Let f(u) = uT Au, where u E Rd and A E Rdxd is a symmetric matrix. Calculate Vuf (u). и
Expert Solution
Step 1: Formula used and given.

Directional derivative: If the function f is differentiable at x, then the directional derivative exists along any vector v and it is given by,

vf(x)=f(x)·v

Given: f(u)=uTAu, ud and Ad×d is symmetric matrix.

To find: uf(u).

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Application of Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning