Algebra Symbols

List of mathematical algebra symbols and signs.

Algebra math symbols table

Symbol Symbol Name Meaning / definition Example
x x variable unknown value to find when 2x = 4, then x = 2
equivalence identical to
equal by definition equal by definition
:= equal by definition equal by definition
~ approximately equal weak approximation 11 ~ 10
approximately equal approximation sin(0.01) ≈ 0.01
proportional to proportional to

f(x) g(x)

lemniscate infinity symbol
much less than much less than 1 1000000
much greater than much greater than 1000000 1
( ) parentheses calculate expression inside first 2 * (3+5) = 16
[ ] brackets calculate expression inside first [(1+2)*(1+5)] = 18
{ } braces set
x floor brackets rounds number to lower integer 4.3= 4
x ceiling brackets rounds number to upper integer 4.3= 5
x! exclamation mark factorial 4! = 1*2*3*4 = 24
| x | single vertical bar absolute value | -5 | = 5
f (x) function of x maps values of x to f(x) f (x) = 3x+5
(fg) function composition

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

f (x)=3x, g(x)=x-1 (f g)(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]
delta change / difference t = t1 - t0
discriminant Δ = b2 - 4ac
sigma summation - sum of all values in range of series xi= x1+x2+...+xn
∑∑ sigma double summation
capital pi product - product of all values in range of series xi=x1∙x2∙...∙xn
e e constant / Euler's number e = 2.718281828... e = lim (1+1/x)x , x→∞
γ Euler-Mascheroni  constant γ = 0.527721566...
φ golden ratio golden ratio constant
π pi constant π = 3.141592654...

is the ratio between the circumference and diameter of a circle

c = π·d = 2·π·r

Linear Algebra Symbols

Symbol Symbol Name Meaning / definition Example
dot scalar product a b
× cross vector product a × b
AB tensor product tensor product of A and B A B
inner product
[ ] brackets matrix of numbers
( ) parentheses matrix of numbers
| A | determinant determinant of matrix A
det(A) determinant determinant of matrix A
|| x || double vertical bars norm
A T transpose matrix transpose

(AT)ij = (A)ji

A Hermitian matrix matrix conjugate transpose

(A)ij = (A)ji

A * Hermitian matrix matrix conjugate transpose

(A*)ij = (A)ji

A -1 inverse matrix A A-1 = I
rank(A) matrix rank rank of matrix A

rank(A) = 3

dim(U) dimension dimension of matrix A

rank(U) = 3

Statistical symbols