## Algebra Symbols

List of mathematical algebra symbols and signs.

## Algebra math symbols table

Symbol Symbol Name Meaning / definition Example xx variable unknown value to find when 2 x= 4, thenx= 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( f∘g)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|a≤x≤b}x∈ [2,6]∆ delta change / difference ∆ t=t_{1 }-t_{0}∆ discriminant Δ = b^{2}- 4ac∑ sigma summation - sum of all values in range of series ∑ x_{i}= x_{1}+x_{2}+...+x_{n}∑∑ sigma double summation ∏ capital pi product - product of all values in range of series ∏ x_{i}=x_{1}∙x_{2}∙...∙x_{n}ee 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×bA⊗Btensor product tensor product of A and B A⊗Binner 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 ( A^{T})= (_{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}=Irank( A)matrix rank rank of matrix A rank( A) = 3dim( U)dimension dimension of matrix A rank( U) = 3

## See also