Given a symmetric matrix(adsbygoogle = window.adsbygoogle || []).push({});

[tex]A=\left(\begin{array}{ccccc}

\sum a_{1s} & & & & \\

& \ddots & & a_{ij} \\

& & \ddots & & \\

&a_{ij} & & \ddots & \\

& & & & \sum w_{as}

\end{array}\right) \in\mathbb{R}^{n\times n},

[/tex]

with strictly positive entries a_{ij}, and with the diagonal entries being sum of off-diagonal entries residing

in the corresponding row/column, how to proceed with the proof for A being positive definite,

[tex]

x^TAx>0

[/tex]

for some non-zero vector x.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Determine if a matrix if positive definite

Loading...

Similar Threads - Determine matrix positive | Date |
---|---|

I Determinant of A^t A | Jun 14, 2016 |

Looking for insight into what the Determinant means... | Oct 30, 2015 |

Determinant of 3x3 matrix equal to scalar triple product? | Sep 3, 2015 |

Determinant and symmetric positive definite matrix | May 26, 2015 |

How to determine an infinitely dimensional matrix is positive definite | Dec 15, 2011 |

**Physics Forums - The Fusion of Science and Community**