# Algebra Symbols

Mastering Algebra: A Visual Guide to Essential Symbols and Notations.

## Algebra math symbols table

Symbol Symbol Name Meaning / definition Example
x x variable unknown value to find when 2 x = 4, then x = 2
= equals sign equality 5 = 2+3
5 is equal to 2+3
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) = 3 x+5
( fg) function composition

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

f ( x)=3 x, 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 = t 1 - t 0
discriminant Δ = b 2 - 4 ac
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
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
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 ( 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 = I
rank( A) matrix rank rank of matrix A rank( A) = 3
dim( U) dimension dimension of matrix A dim( U) = 3
What does the symbol 'x' represent in algebra?

In algebra, the symbol 'x' is often used as a variable to represent an unknown quantity or a placeholder for a value that can vary. It plays a crucial role in solving equations and expressing relationships between quantities.