I am trying to follow the following reasoning:(adsbygoogle = window.adsbygoogle || []).push({});

Given a known matrix A, we want to find w that maximizes the quantity

w'Aw

(where w' denotes the transpose of w) subject to the constraint w'w = 1.

To do so, use a lagrange multiplier, L:

w'Aw + L(w'w - 1)and differentiate to obtain

Aw = Lw.

Thus, we seek the eigenvector of A with the largest eigenvalue.

I do not understand how they differentiated w'Aw + L(w'w-1) to get Aw = Lw. Can someone explain to me what is going on at that step?

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

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

# Maximizing quantity which is a product of matrices/vectors

Loading...

Similar Threads - Maximizing quantity product | Date |
---|---|

I Simple Modules and Maximal Right Ideals ... | Feb 4, 2017 |

I Simple Modules and quotients of maximal modules, Bland Ex 13 | Feb 3, 2017 |

I Finitely Generated Modules and Maximal Submodules | Dec 31, 2016 |

I Prime and Maximal Ideals in PIDs .. Rotman, AMA Theorem 5.12 | Sep 1, 2016 |

Newton's expansion for non-commutative quantities | Feb 3, 2014 |

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