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
= equals sign equality 5 = 2+3
5 is equal to 2+3
not equal sign inequality 5 ≠ 4
5 is not equal to 4
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 yx when y = kx, k constant
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 | vertical bars absolute value | -5 | = 5
f (x) function of x maps 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⇒(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 double sum x
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 = 0.5772156649...  
φ golden ratio golden ratio constant  
π pi constant π = 3.141592654...

is the ratio between the circumference and diameter of a circle

c = πd = 2⋅πr

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 AB
\langle x,y \rangle 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 dim(U) = 3

 

Statistical symbols ►

 


See also

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