Lemma 4.2 Let X be a vector space over K and let (·|·) : X × X → K be a scalar product. The following holds true: (N) The mapping ||x||(--) := V (x|x) : X → R is a norm on X. (CS) |(x|y)| < ||1|l(41)||y|l(1) (x, y E X). (P) ||x + y|l?,1) = |æ|l}?1» + ||!y|/{1,) + 23R(x\y) (x, y E X ). (PI) ||r+ y|l/1,) + |x – y|l?1) 2(|||/1,) + Ily|l/1) (x, y E X ). (CS) is called the Cauchy-Schwarz inequality and (PI) is called the parallelogram identity.
Lemma 4.2 Let X be a vector space over K and let (·|·) : X × X → K be a scalar product. The following holds true: (N) The mapping ||x||(--) := V (x|x) : X → R is a norm on X. (CS) |(x|y)| < ||1|l(41)||y|l(1) (x, y E X). (P) ||x + y|l?,1) = |æ|l}?1» + ||!y|/{1,) + 23R(x\y) (x, y E X ). (PI) ||r+ y|l/1,) + |x – y|l?1) 2(|||/1,) + Ily|l/1) (x, y E X ). (CS) is called the Cauchy-Schwarz inequality and (PI) is called the parallelogram identity.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 60E
Related questions
Question
TASK 23
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning