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eigenfunction

/ˈaɪɡənˌfʌŋkʃən/

Meanings
noun
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." "
math physics science technical function

Related Words

Illustration applied

applied adjective

/əˈplaɪd/

Put into practical use.

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

Illustration function

function noun

/ˈfʌŋ(k)ʃən/ /ˈfʌŋkʃən/

What something does or is used for.

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

Illustration operator

operator noun

/ˈɒpəˌɹeɪtə/ /ˈɑpəˌɹeɪɾɚ/

One who operates.

"The telephone operator answered the call. "

Illustration showing

showing verb

/ˈʃəʊɪŋ/ /ˈʃoʊɪŋ/

To display, to have somebody see (something).

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

Illustration differentiation

differentiation noun

/ˌdɪfəˌɹɛnʃiˈeɪʃən/ /ˌdɪfəˌɹɛnʃiˈeɪʃn̩/

The act of differentiating.

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

Illustration result

result noun

/ɹɪˈzʌlt/

That which results; the conclusion or end to which any course or condition of things leads, or which is obtained by any process or operation; consequence or effect.

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

Illustration lambda

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. "

Illustration scalar

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. "

Illustration eigenvalue

eigenvalue noun

/ˈaɪɡənˌvæljuː/

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.

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

Illustration exponential

exponential noun

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

Any function that has an exponent as an independent variable.

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

Illustration called

called verb

[kɔld]

(heading) To use one's voice.

"The teacher called out my name during attendance. "

Illustration linear

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. "