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A diagonal entry aj j of a symmetric matrix cannot be smaller than all s. If it were
Chapter 6, Problem 6.2.22(choose chapter or problem)
A diagonal entry aj j of a symmetric matrix cannot be smaller than all s. If it were, then Aaj jI would have eigenvalues and would be positive definite. But Aaj jI has a on the main diagonal.
Questions & Answers
QUESTION:
A diagonal entry aj j of a symmetric matrix cannot be smaller than all s. If it were, then Aaj jI would have eigenvalues and would be positive definite. But Aaj jI has a on the main diagonal.
ANSWER:Step 1 of 2
As one necessary and sufficient condition for real symmetric matrix to be positive definite is all the Eigen values of satisfy . Diagonal entry of a symmetric matrix cannot be smaller than all . If it were then would have Positive Eigen values and would be positive definite, this is because Eigen values of are equal to are equal to , where is an arbitrary Eigen value of .