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parisa

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Please give me example of antipodal set in infinite dimensional?

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In summary, an antipodal set in infinite dimensional refers to a set of points in a vector space that are at equal distance from the origin, but in opposite directions. An example of this is the set of all unit vectors in a vector space. It differs from an orthogonal set, which consists of points that are perpendicular to each other but not necessarily on opposite sides of the origin. Antipodal sets can only exist in an infinite dimensional space and have significance in mathematical analysis, optimization, and physics.

- #1

parisa

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Please give me example of antipodal set in infinite dimensional?

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economicsnerd

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What is your definition of an antipodal set?

An antipodal set in infinite dimensional refers to a set of points in a vector space that are at equal distance from the origin, but in opposite directions. In simpler terms, it is a set of points that are on the opposite sides of the origin.

One example of an antipodal set in infinite dimensional is the set of all unit vectors in a vector space. Each of these vectors is at a distance of 1 from the origin, but in opposite directions.

An antipodal set consists of points that are on opposite sides of the origin and are not necessarily perpendicular to each other. On the other hand, an orthogonal set consists of points that are perpendicular to each other but not necessarily on opposite sides of the origin.

No, an antipodal set can only exist in an infinite dimensional space. In a finite dimensional space, there are a limited number of points and therefore, it is not possible to have an infinite number of points on opposite sides of the origin.

Antipodal sets are important in mathematical analysis and optimization as they help in finding solutions to optimization problems. In addition, they also have applications in physics, particularly in the study of quantum mechanics.

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