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Matrices proof help.

  1. Oct 18, 2004 #1

    qaz

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    (i) Let A=A' be an nxn symmetric matrix with distinct eigenvalues la1, la2, ..., lan. Suppose that all eigenvalues lai > 0. Prove that A is positive definite: That is, prove that z'Az > 0 whenever z ne 0. (Hint: Consider the spectral decomposition of A.)

    ???

    (ii) Let A=A' be a 2x2 symmetric matrix with tr(A)>0 and det(A)>0. Prove that A is positive definite. (Hint: Consider the spectral decomposition of A.)

    ???

    i looked at this problem forever, nothing doing for me :cry: :confused: :yuck:
     
  2. jcsd
  3. Oct 18, 2004 #2

    qaz

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    anyone? please help!!!!!!!!!!!!
     
  4. Oct 19, 2004 #3

    matt grime

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    What is the definition of spectral decomposition (and no, I'm not asking out of ignorance)?
     
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