What is Gateaux derivative?
Understand the Problem
The question is asking about the concept of the Gateaux derivative, which is related to functional analysis. It seeks to understand what the Gateaux derivative is and how it is defined or used in mathematical contexts.
Answer
The Gâteaux derivative generalizes the directional derivative.
The Gâteaux derivative is a generalization of the directional derivative, used in mathematics to describe how functions change in locally convex topological vector spaces.
Answer for screen readers
The Gâteaux derivative is a generalization of the directional derivative, used in mathematics to describe how functions change in locally convex topological vector spaces.
More Information
René Gâteaux, after whom the derivative is named, was a French mathematician who was killed in World War I at the age of 25. The Gâteaux derivative extends the concept of directional derivatives in the context of locally convex spaces.
Tips
A common confusion is between the Gâteaux and Fréchet derivatives; the Fréchet derivative requires more conditions like continuity and linearity.
Sources
- Gateaux derivative - Wikipedia - en.wikipedia.org
- Gâteaux Derivative -- from Wolfram MathWorld - mathworld.wolfram.com
- Gateaux Derivative and Directional Derivatives - Math Stack Exchange - math.stackexchange.com
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