Exercise 8.53. Let A be a positive definite n × n matrix. Prove that there exists a number ε 0

Name: Exercise 8.53. Let A be a positive definite n × n matrix. Prove that there exists a number ε > 0 such that if B is any symmetric n × n matrix with ||A - B|| < ε, then B is positive definite.
Uploaded: 2023-05-24T14:44:48-08:00
Duration: 3 min 3 s
Channel: Adi S
Description: Exercise 8.53. Let A be a positive definite n × n matrix. Prove that there exists a number ε > 0 such that if B is any symmetric n × n matrix with ||A - B|| < ε, then B is positive definite.

Question

Exercise 8.53. Let A be a positive definite n × n matrix. Prove that there exists a number ε &gt; 0

Adi S · Accepted Answer

1. Start with the given condition: If B is any symmetric n x n matrix with [A -B|<e, then B is p

Question

Exercise 8.53. Let A be a positive definite $n \times n$ matrix. Prove that there exists a number $\varepsilon > 0$ such that if B is any symmetric $n \times n$ matrix with $||A - B|| < \varepsilon$, then B is positive definite.

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