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PCA

Lagrange Multiplier

  • Statement — maximize \(f(x, y)\) which is subject to \(g(x, y) = 0\)

with the concept showed in the image, we can say that

\[ \begin{gather} \nabla f \parallel \nabla g \\\\ \implies \nabla f = \lambda \nabla g \end{gather} \]

in which \(\lambda\) is known as Lagrange multiplier.