Algebra - vocabulary

Noun

Pronunciation
/ræŋk/ listen

Meaning
A rank is a property of a matrix that tells the dimension of the vector space generated by its columns. This number is the same as the maximal number of linearly independent columns of the matrix. The rank is usually denoted by rank(A), where A is a matrix.

Example
The matrix that has a rank 1 because any pair of columns is linearly dependent.

Etymology
Anglo-Norman and Old French, Middle French renc, ranc, renke, rang with the meaning line (of soldiers), row (of people)

Sources
OED

noun

Pronunciation:

/rɪŋ/

Definition:

Ring is an algebraic structure defined as 5-tuple of set, binary operations on this set (addition and multiplication), one unary operation (addition inverse) and one nullary operation (0). And the following axioms hold.

• addition is associative and commutative
• multiplication is associative
• 0 is the additive identity
• 1 is the multiplicative identity
• a⋅ (b + c) = (a· b) + (a· c) for all a, b, c in R   
• (b + c) · a = (b· a) + (c· a) for all a, b, c in R   

source:

https://dictionary.cambridge.org

noun

Pronunciation:

[ru:t]

Meaning:

a number z such that the value of the polynomial at z equals 0

Source:

https://mathworld.wolfram.com/PolynomialRoots.html