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Some Properties of Affine Sets and Affine Transformations

Gao Jianguang

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Abstract

In this paper,some new concepts and properties abou t affine sets and affine transformations are proposed.For affine sets,the concep t of maximal affinely independent quantities is defined,and we point out the rel ationship between the maximal linearly independent quantities and the maximal af f inely independent quantities in the case of trivial and nontrivial affine sets .For affine transformations,we find that they can be determined uniquely by thei r functions on one affine basis.

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What this paper is about

In this paper,some new concepts and properties abou t affine sets and affine transformations are proposed.For affine sets,the concep t of maximal affinely independent quantities is defined,and we point out the rel ationship between the maximal linearly independent quantities and the maximal af f inely independent quantities in the case of trivial and nontrivial affine sets .For affine transformations,we find that they can be determined uniquely by thei r functions on one affine basis.

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Available abstract

In this paper,some new concepts and properties abou t affine sets and affine transformations are proposed.For affine sets,the concep t of maximal affinely independent quantities is defined,and we point out the rel ationship between the maximal linearly independent quantities and the maximal af f inely independent quantities in the case of trivial and nontrivial affine sets .For affine transformations,we find that they can be determined uniquely by thei r functions on one affine basis.

Key concepts: Affine transformation, Affine hull, Affine coordinate system, Affine combination, Mathematics, Affine group, Affine representation, Affine geometry

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