eigenvalues

/ˈaɪɡənˌvæljuz/

Meanings

noun

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."

Related Words

multiplication noun

/ˌmʌltɪplɪˈkeɪʃən/

The process of computing the sum of a number with itself a specified number of times, or any other analogous binary operation that combines other mathematical objects.

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

transformation noun

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

The act of transforming or the state of being transformed.

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

vector noun

/ˈvɛktə/ /ˈvɛktɚ/

A directed quantity, one with both magnitude and direction; the signed difference between two points.

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

corresponding verb

/ˌkɒɹəˈspɒndɪŋ/ /ˌkɑɹəˈspɑndɪŋ/

(constructed with to) To be equivalent or similar in character, quantity, quality, origin, structure, function etc.

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

operator noun

/ˈɒpəˌɹeɪtə/ /ˈɑpəˌɹeɪɾɚ/

One who operates.

"The telephone operator answered the call. "

lambda noun

/ˈlæm.də/

The eleventh letter of the Classical and Modern Greek alphabet, the twelfth of the Old Greek alphabet.

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

solving verb

/ˈsɒlvɪŋ/ /sɔːlvɪŋ/

To find an answer or solution to a problem or question; to work out.

"The student is solving a math problem. "

square noun

/skwɛə(ɹ)/ /skwɛɚ/

A polygon with four sides of equal length and four right angles; an equilateral rectangle; a regular quadrilateral.

"The floor tiles were arranged in perfect squares. "

eigenvector noun

/ˈaɪɡənˌvɛktər/ /ˈaɪɡənˌvɛktɔːr/

Given a linear transformation T, a vector x such that Ax=\lambda x for some scalar \lambda

"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). "

scalar noun

/ˈskeɪlər/ /ˈskælər/

A quantity that has magnitude but not direction; compare vector

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

exists verb

/ɪɡˈzɪsts/

(stative) to be; have existence; have being or reality

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

linear adjective

/ˈlɪn.i.ə/ /ˈlɪn.i.ɚ/

Having the form of a line; straight or roughly straight; following a direct course.

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