复数complex的magnitude是什么

When A is complex, the elements are sorted by magnitude译为：元素为复数时，按照复数的magnitude排序。

其中magnitude的计算规则如下：

实数的magnitude就是该实数的正平方根，如2的magnitude就是2，-3的magnitude就是3

复数的magnitude是该复数与共轭复数的乘积的正平方根，比如z=3-2j，则magnitude为(3-2j)*(3+2j)的正平方根，也就是9+4＝13的正平方根；

以下为有用的链接：wiki的complex解释

更详细的信息，值得一看：http://frank.mtsu.edu/~phys2020/Lectures/L19-L25/L20/Magnitude/magnitude.html

wiki的complex解释：http://en.wikipedia.org/wiki/Complex_number

GNU的sorting vectors：http://www.gnu.org/software/gsl/manual/html_node/Sorting-vectors.html

matlab中的magnitude解释：http://www.mathworks.cn/cn/help/matlab/ref/abs.html

以下内容为第一个链接中的内容，备份作参考

Consider the complex number z = 21 – 35j. Thecomplex conjugate of the number
z, denoted z*, is obtained by simply taking every j that you see in the expression forz and replacing it by
–j. Thus, in this case, z* = 21 – 35(–j) = 21 + 35j. On the other hand, ifz = 1/(2 – 10j), then
z* = 1/(2 + 10j). It’s easy! Note that the complex conjugate of areal number is just that same real number, since it does not have any
j’s to replace!

The magnitude of a complex number z, denoted |z|, is defined to be the positive square-root of the complex number times its complex conjugate. That is,

In general, for the generic complex number z = a + bj, the magnitude ofz is given by

or, since j2 = –1,

For example, if z = 3 – 2j, then z* = 3 + 2j, and so

Note that the magnitude of a complex number is always areal number. Note also that the magnitude of a real number is just the absolute-value of that real number. For example, ifz = 3, then

while, if z = –2, we get that