Algebra - vocabulary

Noun
Suffix:   -tion

Pronunciation
/ˌpɜːmjʊˈteɪʃən/ listen

Meaning
1) Algebra:

The permutation means the action of rearrangement of the elements for another in a set. More formally: The permutation π in S_n is defined as a bijection from a set S_n onto itself. All permutations of a set with n elements create a symmetric group S_n, where the group operation is function composition. It holds four group axioms for two permutations π and σ in S_n: closure, identity, invertibility, and associativity. The composition of two permutations is not commutative.

2) Combinatorics:

The permutation stands for a number of combinations when the order does not matter following this formula:

Examples

This notation means σ(1) = 2, σ(2) = 5, σ(3) = 4, σ(4) = 3, and σ(5) = 1

This figure depicts the graphical illustration of the notation.

Similar words
to permutate     /'pəːmjʊteɪt/         verb
permutability    /pəˌmjuːtə'bɪlɪti/    noun           condition of being permutable
permutable       /pər'mjutəbəl/       adjective    it is possible to permutate it
permutant         /pə'mjuːtənt/         noun           the result from permutation
permutated       /'pəːmjʊteɪtɪd/      adjective    it has been subjected to permutation
permutating      /'pəːmjʊteɪtɪŋ/      adjective    undergoing permutation

Related terms
Even permutation
Odd permutation

Etymology
From French permutation, Latin permūtātiōn-, permūtātiō, Anglo-Norman permutacioun, Anglo-Norman and Middle French permutacion

Sources
OED
Figure

Noun, (verb - see below)

Pronunciation
/'pɪvət/ listen

Synonym
Pivot element

Meaning
A pivot is an element on the left-hand side of a matrix for solving a system of linear equations using the Gaussian elimination that you want the elements above and below to be zero.

Example
The green 3 is a pivot. The aim is to make yellow numbers into zero.

Similar words
To pivot      /'pɪvət/           verb        to make an element above or below a leading one into a zero
Pivoting      /'pɪvətɪŋ/       noun       a process of  making an element above or below a leading one into zero

Etymology
Middle French, French pivot, hinge (1338; 1174–78 in figurative use in the name of a dance), vertical main root of a fruit tree (1651), officer around whom troops wheel (1752)

Source:
OED

n. and adj.

Pronunciation

Meaning

Originally: an expression consisting of many terms, a multinomial. Now: spec. a sum of one or more terms each consisting of a constant multiplied by one or more variables raised to a positive (or non-negative) integral power (e.g. x4 − 3x2y + 7).

Etymology

Origin: Formed within English, by compounding. Etymons: poly-,  -nomial 

OED

noun

Pronunciation:

[prʌɪm]

Meaning:

a positive integer greater than 1 which can be divided without a remainder only by numbers 1 and itself

Source:

https://www.oed.com/view/Entry/266923#eid71284393

noun

Pronunciation:

/prəˈdʒekʃ(ə)n/

Definition:

The linear operation, which two-times implicated gives the same result as identical operation is called projection.

Sorce:

https://www.macmillandictionary.com