Hi ! Need help with a matrix problem.

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#1
Show that matrix D = E′AE is positive semidefinite for any 3 × 2 matrix E. Which condition needs matrix E to satisfy such that matrix D is positive definite?
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1 month ago
#2
(Original post by eeieei14)
Show that matrix D = E′AE is positive semidefinite for any 3 × 2 matrix E. Which condition needs matrix E to satisfy such that matrix D is positive definite?
Is that really the question / what is A?
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#3
(Original post by mqb2766)
Is that really the question / what is A?
apologies - forgot to include this. would appreciate any help on this - spent the last day trying to figure out how to answer this question.
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1 month ago
#4
(Original post by eeieei14)
apologies - forgot to include this. would appreciate any help on this - spent the last day trying to figure out how to answer this question.
The starting point is obviously to consider the symmetry of the expression in E. Then think about the structure of A. What have you covered about positive definite and do you know how to show
E'E
(so A = I, the identity matrix) is positive definite?

Im being lax with leaving out semis ...
Last edited by mqb2766; 1 month ago
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#5
thank you so much that was super helpful
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