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Show that an orthogonal transformation L from Rn to Rw preserves angles: The angle

Linear Algebra with Applications | 4th Edition | ISBN: 9780136009269 | Authors: Otto Bretscher ISBN: 9780136009269 434

Solution for problem 29 Chapter 5.3

Linear Algebra with Applications | 4th Edition

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Linear Algebra with Applications | 4th Edition | ISBN: 9780136009269 | Authors: Otto Bretscher

Linear Algebra with Applications | 4th Edition

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Problem 29

Show that an orthogonal transformation L from Rn to Rw preserves angles: The angle between two nonzero vectors v and w in Rfl equals the angle between L(v) and L(w). Conversely, is any linear transformation that preserves angles orthogonal?

Step-by-Step Solution:
Step 1 of 3

L22 - 6 Geometrically f(x +∆ x) y = f(x) f(x) x x +∆ x f(x +∆ x)= f(x +∆ x) ≈

Step 2 of 3

Chapter 5.3, Problem 29 is Solved
Step 3 of 3

Textbook: Linear Algebra with Applications
Edition: 4
Author: Otto Bretscher
ISBN: 9780136009269

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Show that an orthogonal transformation L from Rn to Rw preserves angles: The angle