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Inverse of a positive semi-definite matrix?

  1. Dec 5, 2012 #1
    If A is some nonsquare matrix that is possible rank-deficient, then am I right to understand that (A^T)(A) is a positive semidefinite matrix? Does there exist an inverse (A^T A)^-1?

    Thanks for any help
  2. jcsd
  3. Dec 5, 2012 #2

    D H

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    Any real nxm matrix A will have ATA (and AAT) be positive semidefinite.

    Now let A be some matrix all of whose elements are zero. Obviously both ATA and AAT will also be zero matrices (but now square), and obviously, no inverse.

    There's a world of difference between positive definite and positive semidefinite.
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