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eigenfunction

/ˈaɪɡənˌfʌŋkʃən/

Meanings
noun

特征函数, 本征函数

A function \phi such that, for a given linear operator D, D\phi=\lambda\phi for some scalar \lambda (called an eigenvalue).

Examples :

""When the 'differentiation' operator is applied to the exponential function e<sup>2xsup>, the result is 2e<sup>2xsup>, showing that e<sup>2xsup> is an eigenfunction of the differentiation operator with eigenvalue 2." "
当“求导”算符作用于指数函数 e<sup>2xsup> 时，结果是 2e<sup>2xsup>，这表明 e<sup>2xsup> 是求导算符的特征函数 (eigenfunction)，其对应的特征值 (eigenvalue) 为 2。
math physics science technical function

Related Words

Illustration applied

applied adjective

/əˈplaɪd/

实际应用的，应用的

"The new math strategies were applied successfully in the classroom. "

新的数学策略在课堂上得到了成功的实际应用。

Illustration function

function noun

/ˈfʌŋ(k)ʃən/ /ˈfʌŋkʃən/

功能，作用.

"The function of a school lunch is to provide students with nutrition. "

学校午餐的功能是为学生提供营养。

Illustration operator

operator noun

/ˈɒpəˌɹeɪtə/ /ˈɑpəˌɹeɪɾɚ/

操作员， 经营者

"The telephone operator answered the call. "

电话接线员接听了电话。

Illustration showing

showing verb

/ˈʃəʊɪŋ/ /ˈʃoʊɪŋ/

展示，显现，表明。

"All he had to show for four years of attendance at college was a framed piece of paper."

他上了四年大学，最终能拿出来展示的，就只有一张装在镜框里的纸。

Illustration differentiation

differentiation noun

/ˌdɪfəˌɹɛnʃiˈeɪʃən/ /ˌdɪfəˌɹɛnʃiˈeɪʃn̩/

区分，分化

"In school, the teacher uses differentiation to help students learn at their own pace, providing easier or more challenging tasks based on individual needs. "

在学校里，老师会使用差异化教学来帮助学生按照自己的节奏学习，根据每个学生的具体需求，提供更简单或更具挑战性的任务。

Illustration result

result noun

/ɹɪˈzʌlt/

结果，后果，成果.

"the result of a course of action;  the result of a mathematical operation"

一项行动的结果; 一项数学运算的成果

Illustration lambda

lambda noun

/ˈlæm.də/

Lambda，第十一个希腊字母。

"In Greek class today, we learned that lambda is the eleventh letter in their alphabet. "

今天希腊语课上，我们学到lambda是他们字母表里的第十一个字母。

Illustration scalar

scalar noun

/ˈskeɪlər/ /ˈskælər/

标量，无向量。

"The recipe only needs the scalar quantity of two cups of flour, not the direction in which to pour it. "

这个食谱只需要两杯面粉这个标量的数量，而不需要说明倒入的方向。

Illustration eigenvalue

eigenvalue noun

/ˈaɪɡənˌvæljuː/

特征值

"The eigenvalues lambda of a square transformation matrix mathrm{M} may be found by solving det(mathrm{M} - lambdamathrm{I}) = 0."

对于一个方阵变换矩阵M，它的特征值λ可以通过解行列式det(M - λI) = 0 来找到。

Illustration exponential

exponential noun

/ˌɛk.spəʊ.ˈnɛn.tʃəl/ /ˌɛk.spoʊ.ˈnɛn.tʃəl/

指数函数

"The graph of 2 to the power of x demonstrates an exponential that increases rapidly as x grows. "

2的x次方的图像展示了一个指数函数，它随着x的增长而迅速增加。

Illustration called

called verb

[kɔld]

喊，叫。

"The teacher called out my name during attendance. "

点名的时候，老师喊了我的名字。

Illustration linear

linear adjective

/ˈlɪn.i.ə/ /ˈlɪn.i.ɚ/

线性的，直线的。

"The path to the park follows a linear route, going straight down the street. "

去公园的路是直线的，沿着街道笔直地走。