复数complex的magnitude是什么 |
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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
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