(i) Let A be an n n symmetric matrix such that A and I n ...
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(i) Let A be an n × n symmetric matrix such that A and In – A are both positive semi-definite. Show that 0 ≤ aii ≤ 1 for i = 1, . . . , n, where αii is the ith diagonal element of A.
(ii) Prove that if A is an n × n symmetric, idempotent matrix then it must be positive semi-definite.
(iii) Prove that the only n × n symmetric, idempotent matrix that is also invertible is In.
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i The symmetric matrix A is positive semidefinite if and only if v T Av 0 fo...View the full answer
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Introductory Econometrics A Modern Approach
ISBN: 9781337558860
7th Edition
Authors: Jeffrey Wooldridge
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