Empowering a brighter world through superior education is our commitment.

Online Calculators & Tools

Algebra Symbols

List of mathematical algebra symbols and signs.

Algebra math symbols table

SymbolSymbol NameMeaning / definitionExample
xx variableunknown value to findwhen 2x = 4, then x = 2
=equals signequality5 = 2+3
5 is equal to 2+3
not equal signinequality5 ≠ 4
5 is not equal to 4
equivalenceidentical to 
equal by definitionequal by definition 
:=equal by definitionequal by definition 
~approximately equalweak approximation11 ~ 10
approximately equalapproximationsin(0.01) ≈ 0.01
proportional toproportional toyx when y = kx, k constant
lemniscateinfinity symbol 
much less thanmuch less than1 ≪ 1000000
much greater thanmuch greater than1000000 ≫ 1
( )parenthesescalculate expression inside first 2 * (3+5) = 16
[ ]bracketscalculate expression inside first [(1+2)*(1+5)] = 18
{ }bracesset 
xfloor bracketsrounds number to lower integer⌊4.3⌋= 4
xceiling bracketsrounds number to upper integer⌈4.3⌉= 5
x!exclamation markfactorial4! = 1*2*3*4 = 24
| x |vertical barsabsolute value| -5 | = 5
f (x)function of xmaps values of x to f(x)f (x) = 3x+5
(fg) function composition

(fg) (x) = f (g(x))

f (x)=3x,g(x)=x-1⇒(fg)(x)=3(x-1) 
(a,b)open interval(a,b) = {x | a < x < b}x ∈ (2,6)
[a,b]closed interval[a,b] = {x | axb}x ∈ [2,6]
deltachange / differencet = t1- t0
discriminantΔ = b2 - 4ac 
sigmasummation - sum of all values in range of series xi= x1+x2+...+xn
∑∑sigmadouble summationdouble sum x
capital piproduct - product of all values in range of seriesxi=x1∙x2∙...∙xn
ee constant / Euler's numbere = 2.718281828...e = lim (1+1/x)x , x→∞
γEuler-Mascheroni constantγ = 0.5772156649... 
φgolden ratiogolden ratio constant 
πpi constantπ = 3.141592654...

is the ratio between the circumference and diameter of a circle

c = πd = 2⋅πr

Linear Algebra Symbols

SymbolSymbol NameMeaning / definitionExample
·dotscalar producta · b
×crossvector producta × b
ABtensor producttensor product of A and BAB
\langle x,y \rangleinner product  
[ ]bracketsmatrix of numbers 
( )parenthesesmatrix of numbers 
| A |determinantdeterminant of matrix A 
det(A)determinantdeterminant of matrix A 
|| x ||double vertical barsnorm 
ATtransposematrix transpose(AT)ij = (A)ji
AHermitian matrixmatrix conjugate transpose(A)ij = (A)ji
A*Hermitian matrixmatrix conjugate transpose(A*)ij = (A)ji
A-1inverse matrixA A-1 = I 
rank(A)matrix rankrank of matrix Arank(A) = 3
dim(U)dimensiondimension of matrix Adim(U) = 3

 

Statistical symbols