Hessian Meaning: Definition, Examples, and Translations
🧮
hessian
[ˈhɛs.ɪən ]
Definitions
mathematics
In mathematics, a Hessian refers to the square matrix of second-order partial derivatives of a scalar-valued function. It is primarily used in optimization problems to determine the local curvature of a function and helps in identifying local minima and maxima. The Hessian is crucial in the field of multivariable calculus, particularly in second-order optimization algorithms. Analyzing the eigenvalues of the Hessian can reveal the nature of critical points.
Synonyms
curvature matrix, second derivative matrix.
Examples of usage
- The Hessian matrix indicates whether a function has a local minimum.
- To analyze the stability, we compute the Hessian of the dynamical system.
- The Hessian is essential in Newton's method for optimization.
textiles
A Hessian is also a type of coarse, heavy fabric made from jute or other materials. It is often used for making sacks and heavy-duty items due to its strong and durable nature. The fabric is recognized for its hessian weave, giving it a distinctive rough texture. This material is commonly seen in agriculture, construction, and packaging.
Synonyms
burlap, jute fabric.
Examples of usage
- The potatoes were stored in hessian sacks.
- We used hessian for the garden project.
- Hessian fabric is environmentally friendly and biodegradable.
Translations
To see the translation, please select a language from the options available.
Origin of 'hessian'
The term 'Hessian' in mathematics is derived from the name of the famous German mathematician Ludwig Otto Hesse (1811-1874), who contributed significantly to the theories of algebra and multivariable calculus. The Hessian matrix itself became fundamental in the analysis of multivariable functions, especially in the context of optimization. In textiles, the term 'Hessian' comes from the Historical Landgraviate of Hesse in Germany, where hessian fabric was originally produced. The material's use dates back to the 19th century, primarily utilitarian, reflecting the regional production of coarse fabrics. Today, both meanings of the term 'Hessian' are well-established in their respective fields, contributing to mathematical theory and practical applications in various industries.