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1. Let A be a real n x n symmetric matrix, (a) Prove that if A is positive definite, A is invertible.

1. Let A be a real n x n symmetric matrix, (a) Prove that if A is positive definite, A is invertible.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.5: Applications
Problem 30EQ
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1. Let A be a real n x n symmetric matrix, (a) Prove that if A is positive definite, A is invertible. (b) Using Schur's theorem to prove that A is diagonalizable. (c) Let A = 21 1 1 2 1 find a matrix B such that A = B^B. 1 2 1
Transcribed Image Text:1. Let A be a real n x n symmetric matrix, (a) Prove that if A is positive definite, A is invertible. (b) Using Schur's theorem to prove that A is diagonalizable. (c) Let A = 21 1 1 2 1 find a matrix B such that A = B^B. 1 2 1
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