英语翻译Choose a positive integer n.Put the n points which divid

英语翻译
Choose a positive integer n.Put the n points which divide the unit circle（单位圆） into n equal parts.Let be the image of under the transformation defined by the matrix
Draw the lines form the origin O to all the n points .And draw line segments from each to its image .(To make the graph clearer you may draw all the in red and all the in black.)
Observe the difference between the directions of each vector and and thus know how the direction of changes to that of .Is there any having the same directions as its image If so,how many are there then?
In the course of linear algebra one learns that if a nonzero vector is sent to parallel to（平行于） u by a linear transformation namely,if the direction of and are the same or opposite or ,and thus for a scalar ,then is called an eigenvector（特征向量） of ,while the scalar is called the eigenvalue（特征值）.If one observes a vector having the same direction as its image ,then this is an eigenvector of .(If and have the opposite direction ,is also an eigenvector.)
有些公式打不出来..
逐句翻译也可，只要通顺能明白什么意思就OK