bilinear field (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun

Phonetic Transcription

/bɪˈlaɪnɪər fiːld/

Meaning and Use

A "bilinear field" refers to a mathematical concept often used in the context of bilinear forms in linear algebra or functional analysis. It describes a type of function that is linear in each of its arguments. Typically, a bilinear field can arise in contexts such as vector spaces or in the study of quadratic forms.

Frequency of Use

The term "bilinear field" is relatively specialized and is primarily found in academic and mathematical contexts. It is used more often in written texts, especially in mathematical literature, journals, textbooks, and coursework. Its occurrence in oral speech is relatively low, as the concept is often discussed in more specialized discussions.

Example Sentences

1. A bilinear field can be useful in defining quadratic forms.

2. Билинейное поле может быть полезным для определения квадратичных форм.

3. In programming, we can implement a bilinear field to optimize certain computations.

4. В программировании мы можем реализовать билинейное поле для оптимизации некоторых вычислений.

5. Researchers are exploring the properties of a bilinear field in advanced theoretical physics.

6. Исследователи изучают свойства билинейного поля в области теоретической физики.

Idiomatic Expressions

While "bilinear field" itself is not a common component of idiomatic expressions, it is closely linked to several mathematical concepts that can be expressed in idiomatic patterns within academic discourse.

Example Sentences with Idiomatic Expressions

1. In a bilinear field, you can say that the inner product behaves like a well-defined operation.

2. В билинейном поле можно сказать, что внутреннее произведение ведет себя как хорошо определенная операция.

3. When dealing with a bilinear field, one must tread carefully to avoid misinterpretations.

4. Имея дело с билинейным полем, нужно быть осторожным, чтобы избежать неправильных толкований.

5. Understanding the intricacies of a bilinear field opens up new avenues in mathematical research.

6. Понимание intricacies билинейного поля открывает новые пути в математических исследованиях.

7. One shouldn't underestimate the power of a bilinear field in solving complex equations.

8. Не следует недооценивать силу билинейного поля в решении сложных уравнений.

Etymology

The term "bilinear" is derived from "bi-" meaning two, and "linear" from the Latin "linearis", which means "pertaining to lines". "Field" comes from the Old English "feld", referring to an open land or area, which has been adapted in mathematics to indicate a set with certain algebraic properties.

Synonyms and Antonyms

Synonyms: - Bilinear form - Bilinear map

Antonyms: - Non-linear function - Quadratic field (in certain contexts)