[SciPy-user] howto construct matrix A: dot(A.T, A) is positive-definite

Anne Archibald peridot.faceted@gmail....
Fri Oct 5 09:45:15 CDT 2007


On 05/10/2007, lorenzo bolla <lbolla@gmail.com> wrote:
> for every A, dot(A.T, A) is always semi positive definite.
> it is strictly positive definite if it hasn't a zero eigenvalue.
> make sure your A doesn't have a zero eigenvalue.
> (if your A is sparse, as it seems, it could have at least one row or one
> column filled with zeros, hence a zero eigenvalue).

Also, if A is n by m, then dot(A.T, A) will be m by m, but its rank
will be at most min(m,n). So in particular if n<m then dot(A.T,A) will
never be positive definite. dot(A,A.T) may be.

Anne


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