“Involuntary”的概念、定义、习题解题方法及翻译-数学辞典

单词

Involuntary

释义

Involuntary

A Linear Transformation of period two. Since a Linear Transformation has the form,

(1)

applying the transformation a second time gives

(2)

For an involuntary,

, so

(3)

Since each Coefficient must vanish separately,

The first equation gives

. Taking

would require

, giving

, the identity transformation. Taking

gives

, so

(7)

the general form of an Involution.

See also Cross-Ratio, Involution (Line)

References

Woods, F. S. Higher Geometry: An Introduction to Advanced Methods in Analytic Geometry. New York: Dover, pp. 14-15, 1961.

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