HILBERT SPACE Meaning and
Definition
-
A Hilbert space is a concept in mathematics that refers to an abstract vector space equipped with an inner product, which allows for the measurement of angles and lengths of vectors within the space. Named after the German mathematician David Hilbert, this mathematical construct provides a framework for analysis and is frequently utilized in various branches of physics, particularly quantum mechanics.
Formally, a Hilbert space is a complete inner product space, meaning that it is equipped with a norm induced by the inner product that satisfies the completeness condition. This completeness ensures that Cauchy sequences in the space converge to a limit that is also within the space. The inner product defines the notion of orthogonality, where two vectors are considered orthogonal if their inner product is zero.
Hilbert spaces have a wide range of applications, including the representation of physical states in quantum mechanics, signal processing, and harmonic analysis. They provide a mathematical environment wherein the concept of orthogonality and convergence can be studied rigorously, allowing for the formulation and solution of various mathematical problems.
In summary, a Hilbert space is a complete inner product vector space that relies on an inner product to measure angles and distances between vectors. It plays a significant role in mathematics and physics, particularly in the context of quantum mechanics.
Common Misspellings for HILBERT SPACE
- gilbert space
- bilbert space
- nilbert space
- jilbert space
- uilbert space
- yilbert space
- hulbert space
- hjlbert space
- hklbert space
- holbert space
- h9lbert space
- h8lbert space
- hikbert space
- hipbert space
- hiobert space
- hilvert space
- hilnert space
- hilhert space
- hilgert space
Etymology of HILBERT SPACE
The word "Hilbert Space" is named after the German mathematician David Hilbert (1862-1943). The term was coined by Hilbert in the early 20th century when he introduced and developed the mathematical concept of a Hilbert space, which is a particular type of mathematical space used in functional analysis and quantum mechanics. Hilbert made significant contributions to the field of mathematics, and his work on Hilbert spaces has had a lasting impact on various branches of mathematics and physics.
Infographic
Add the infographic to your website:
