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Use one of the equiv statements to conclude that the matrix below is not a positive definite matrix. Explain! B = 1 2 3 204 341

Use one of the equiv statements to conclude that the matrix below is not a positive definite matrix. Explain! B = 1 2 3 204 341

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 61E
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Definition A matrix A E R"x" is said to be positive definite if it is symmetric and has an LU factorization in which each pivot is positive. The following statements are equivalent: (i) A is positive definite. A can be factored as A diagonal entries. TAx> 0 for all nonzero xER". Use one of the equiv statements to conclude that the matrix below is not a positive definite matrix. Explain! - RTR where R is an upper triangular matrix with positive B = 1 2 3 204 3 4 1
Transcribed Image Text:Definition A matrix A E R"x" is said to be positive definite if it is symmetric and has an LU factorization in which each pivot is positive. The following statements are equivalent: (i) A is positive definite. A can be factored as A diagonal entries. TAx> 0 for all nonzero xER". Use one of the equiv statements to conclude that the matrix below is not a positive definite matrix. Explain! - RTR where R is an upper triangular matrix with positive B = 1 2 3 204 3 4 1
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