Algebra - vocabulary

n.

Pronunciation

ˈīgənˌvalyo͞o

Meaning

One of those special values of a parameter in an equation for which the equation has a solution.

Etymology

translating German eigenwert

www.oed.com

Noun
Prefix: eigen-

Pronunciation
/'ʌɪɡ(ə)nˌvɛktə/ listen

Synonym
Characteristic vector of a linear transformation

Meaning
An eigenvector is a nonzero vector that is changed at most by a scalar factor after the application of a linear transformation. It satisfies the formula Av = λv, where A is a matrix, λ is a scalar (eigenvalue) and v is the eigenvector.

Example
This figure displays the matrix A acting on the vector x. The direction of the vector remains; thus, the x is the eigenvector of A.

Etymology
German eigen (own), from adoptions or partial translations of German compounds in Mathematics and Physics.

Sources
OED
Figure from WIKIPEDIA

Noun
Suffix: -ing

Pronunciation
/ɪm'bɛdiŋ/ listen

Meaning
The action of giving some mathematical structure in another (a subgroup in a group).

Example
The map f is an embedding in the following:

The embedding is denoted by the use of a hooked arrow.

Similar words:
embed (also imbed)                         verb              listen
embedded (also imbedded)          adjective     listen 
embeddable (also imbeddable)    adjective     listen

Etymology
First in the paper 1939 Duke Math. Jrnl. Isometric embedding of flat manifolds in Euclidian space.

Source
OED