eigenvalue background
BeDict Logo

eigenvalue

/ˈaɪɡənˌvæljuː/

Meanings
noun

特征值

A scalar, \lambda, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a given linear operator \mathrm{A} is equal to the image of x under multiplication by \lambda; i.e. \mathrm{A} x = \lambda x.

Examples :

"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。
math physics technical

Related Words

Illustration multiplication

multiplication noun

/ˌmʌltɪplɪˈkeɪʃən/

乘法，相乘。

"In math class, we learned that multiplication is a quick way to add the same number many times. "

在数学课上，我们学到乘法是一种快速计算相同数字多次相加的方法。

Illustration transformation

transformation noun

/ˌtɹæns.fə(ɹ)ˈmeɪ.ʃən/ /ˌtɹæns.fɔɹˈmeɪ.ʃən/

转变，转化，变革

"The transformation of the classroom from a noisy space to a quiet learning environment was remarkable. "

教室从喧闹的空间转变为安静的学习环境，这种转变非常显著。

Illustration vector

vector noun

/ˈvɛktə/ /ˈvɛktɚ/

向量, 矢量

"The wind's vector pointed directly north at 15 miles per hour, making it hard to ride my bike home. "

风的矢量指向正北，时速15英里，这让骑自行车回家变得很困难。(Fēng de shǐliàng zhǐxiàng zhèng běi, shísù 15 yīnglǐ, zhè ràng qí zìxíngchē huí jiā biàn dé hěn kùnnan.)

Illustration eigenvalues

eigenvalues noun

/ˈaɪɡənˌvæljuz/

特征值

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

要找到方阵变换矩阵M的特征值λ，可以通过解方程det(M - λI) = 0 来实现。(其中I是单位矩阵)。

Illustration corresponding

corresponding verb

/ˌkɒɹəˈspɒndɪŋ/ /ˌkɑɹəˈspɑndɪŋ/

相符，相应。

"The student's performance on the math test corresponded to the level of effort she put in during the week. "

这位学生在数学考试中的表现与她这周付出的努力程度相符。

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 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 solving

solving verb

/ˈsɒlvɪŋ/ /sɔːlvɪŋ/

解决，解答，解开。

"The student is solving a math problem. "

学生正在解答一道数学题。

Illustration eigenvector

eigenvector noun

/ˈaɪɡənˌvɛktər/ /ˈaɪɡənˌvɛktɔːr/

特征向量

"When stretching a photograph horizontally, an eigenvector of the transformation could be a vertical line; it remains a vertical line, only changing in length (or possibly direction, if the scaling factor is negative). "

当水平拉伸一张照片时，这种变换的特征向量可能是一条垂直线；它仍然保持为一条垂直线，只是长度发生了改变（或者，如果缩放因子是负数，方向可能也会改变）。

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 exists

exists verb

/ɪɡˈzɪsts/

存在，生存.

"Simple: "Life exists on Earth." Slightly more specific, but still easy to understand: "My old school still exists, even though it's been remodeled." "

我的老学校虽然被重新装修过了，但仍然存在。

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。