Negative Semi-Definite Matrix: Difference between revisions

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* <B>Example(s)</U>:</B>
* <B>Example(s)</U>:</B>
** <math>\begin{bmatrix} -2 & -2 & -2 \\ -2 & -6 & -2 \\ -2 & -2 & -2 \end{bmatrix}</math> is a Negative Semi-Definite matrix with [[eigenvalues]] -8, -2 and 0.
** <math>\begin{bmatrix} -2 & -2 & -2 \\ -2 & -6 & -2 \\ -2 & -2 & -2 \end{bmatrix}</math> is a Negative Semi-Definite matrix with [[eigenvalues]] -8, -2 and 0.
* <B>Counter-Example(s)</U>:</B>
** <math>\begin{bmatrix} 2 & 2 & 2 \\ 2 & 6 & 2 \\ 2 & 2 & 2 \end{bmatrix}</math> is not a Negative Semi-Definite matrix.
* <B>See:</B> [[Positive Definite Matrix]].
* <B>See:</B> [[Positive Definite Matrix]].
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Revision as of 13:29, 6 January 2016

A Negative Semi-Definite Matrix is a symmetric matrix whose eigenvalues are nonpositive.

  • Context:
    • It can also be stated as: A matrix [math]\displaystyle{ A }[/math] is called Negative Semi-Definite if [math]\displaystyle{ -A }[/math] is positive semi-definite matrix.
  • Example(s):
    • [math]\displaystyle{ \begin{bmatrix} -2 & -2 & -2 \\ -2 & -6 & -2 \\ -2 & -2 & -2 \end{bmatrix} }[/math] is a Negative Semi-Definite matrix with eigenvalues -8, -2 and 0.
  • Counter-Example(s):
    • [math]\displaystyle{ \begin{bmatrix} 2 & 2 & 2 \\ 2 & 6 & 2 \\ 2 & 2 & 2 \end{bmatrix} }[/math] is not a Negative Semi-Definite matrix.
  • See: Positive Definite Matrix.


References

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