Hessian: meaning, definitions and examples
๐งฎ
hessian
[ หhษs.ษชษn ]
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
Translations of the word "hessian" in other languages:
๐ต๐น hessiano
๐ฎ๐ณ เคนเฅเคธเคฟเคฏเคจ
๐ฉ๐ช Hessian
๐ฎ๐ฉ hessian
๐บ๐ฆ ะณะตััะธะฐะฝะต
- ะณะตััะธะฐะฝะบะฐ
- ะณะตััะธะฐะฝ
๐ต๐ฑ hesjan
๐ฏ๐ต ใใใทใขใณ
๐ซ๐ท hessien
๐ช๐ธ hesiano
๐น๐ท hesyan
๐ฐ๐ท ํค์์
๐ธ๐ฆ ูุณูุงู
๐จ๐ฟ hessian
๐ธ๐ฐ hessian
๐จ๐ณ ๆตทๆฃฎ
๐ธ๐ฎ hesijan
๐ฎ๐ธ hessian
๐ฐ๐ฟ ะณะตััะธะฐะฝ
๐ฌ๐ช แฐแแกแแแแ
๐ฆ๐ฟ hesyan
๐ฒ๐ฝ hesiano
Etymology
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.