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Algebra Symbols

 

Algebra is a branch of mathematics that deals with symbols and the rules that govern their use. These symbols are known as variables in algebra because they represent quantities with no set values. Equations in mathematics explain relationships between variables in the same way that sentences indicate relationships between specific words. It is critical to understanding the important mathematical symbols and terminology used in algebra.

Symbols in Algebra and their Names

Let's look at the names of some popular algebra symbols that are used in both basic and advanced algebra.

Algebraic Symbol Name Definition of the symbol Example (if necessary)
x x variable unknown value to find when 3 x = 6, then x = 2
:= equal by definition equal by definition  
approximately equal approximation sin (0.02) ≈ 0.02
proportional to proportional to y ∝ x when y = ax, a constant
~ approximately equal weak approximation 10.2 ~ 10
equal by definition equal by definition  
[ ] brackets calculate expression inside first [(1+3)*(1+4)] = 20
much greater than much greater than 500000 ≫ 1
( ) parentheses calculate expression inside first 2 * (3+4) = 14
⌊ x ⌋ floor brackets rounds number to lower integer ⌊3.2⌋= 3
lemniscate infinity symbol  
equivalence identical to  
| x | single vertical bar absolute value | -9 | = 9
much less than much less than 1 ≪ 8000000
{ } braces set  
⌈ x ⌉ ceiling brackets rounds number to upper integer ⌈4.1⌉= 5
f ( x ) function of x maps values of x to f(x) f ( x ) = 7x +8
( f ∘ g ) function composition ( f ∘ g ) ( x ) = f ( g ( x )) f ( x )=8 x , g ( x )= x-4 ⇒( f ∘ g )( x )=8( x -4)
( a , b ) open interval ( a , b ) = { x | a < x < b } x ∈ (1,5)
[ a , b ] closed interval [ a , b ] = { x | a ≤ x ≤ b } x ∈ [0,5]
delta change / difference ∆ t = t 1 – t 0
sigma summation – sum of all values in range of series ∑ x i = x 1 +x 2 +…+x n
e e constant / Euler’s number e = 2.718281828… e = lim (1+1/ x) x, x → ∞
discriminant Δ = b 2 – 4 ac  
capital pi product – product of all values in range of series ∏ x i =x 1 ∙x 2 ∙…∙x n
π pi constant π = 3.141592654… is the ratio between the circumference and diameter of a circle c = π · d = 2· π · r
∑∑ sigma double summation ∑ 2 j = 1 ∑ 8 i = 1 x i , j = ∑ 8 i = 1 x i , j + ∑ 8 i = 1 x i , 2
γ Euler-Mascheroni constant γ = 0.527721566…  
φ golden ratio golden ratio constant  
Symbol Symbol Name Meaning/definition Example
A -1 inverse matrix A A -1 = I  
× cross vector product a × b
⟨ x , y ⟩ < inner product    
rank( A ) matrix rank rank of matrix A rank( A ) = 4
dot scalar product a ∙ b
det(A) determinant determinant of matrix A  
[ ] brackets matrix of numbers  
( ) parentheses matrix of numbers  
A ⊗ B tensor product tensor product of A and B A ⊗ B
A T transpose matrix transpose (AT)ij = (A)ji
A † Hermitian matrix matrix conjugate transpose (A†) ij = (A) ji
| A | determinant determinant of matrix A  
|| x || double vertical bars norm  
dim(U) dimension dimension of matrix A rank(U) = 5
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