“Linear Transformation”的概念、定义、习题解题方法及翻译-数学辞典

单词

Linear Transformation

释义

Linear Transformation

An Matrix is a linear transformation (linear Map) Iff, for every pair of-Vectors and and every Scalar ,

(1)

and

(2)

Consider the 2-D transformation

			(3)
			(4)

Rescale by defining

and

, then the above equations become

(5)

where

and

are defined in terms of the oldconstants. Solving for

gives

(6)

so the transformation is One-to-One. To find the Fixed Points of the transformation,set

to obtain

(7)

This gives two fixed points which may be distinct or coincident. The fixed points are classified as follows.

See also Elliptic Fixed Point (Map), Hyperbolic Fixed Point (Map), Involuntary, Linear Operator, Parabolic Fixed Point

References

Woods, F. S. Higher Geometry: An Introduction to Advanced Methods in Analytic Geometry. New York: Dover, pp. 13-15, 1961.

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