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TRUE OR FALSE If matrix A is similar to B and A is orthogonal, then B must be orthogonal

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

Solution for problem 37 Chapter 5

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 37

TRUE OR FALSE? If matrix A is similar to B and A is orthogonal, then B must be orthogonal as well.

Step-by-Step Solution:
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M303 Section 5.1 Notes- Introduction to “Eigenstuff”; Diagonalization 11-30-16  From here on, only consider square matrices ( )  If is × , then gives rise to liner map :ℝ → ℝ givn by = o Since source and target dimensions are identical, can compare inputs and outputs  Focus on vectors on which has particularly simple effect  Eigenvector of matrix - nonzero vector such that = , where ℝ o uniquely determined and called the eigenvalue of (for ); we call a -eigenvector o Eigenvalues of are scalars for which there

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Chapter 5, Problem 37 is Solved
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Textbook: Linear Algebra with Applications
Edition: 4
Author: Otto Bretscher
ISBN: 9780136009269

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TRUE OR FALSE If matrix A is similar to B and A is orthogonal, then B must be orthogonal