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	y ∝ x 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
(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 = 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 = 0.5772156649...
φ	golden ratio	golden ratio constant
π	pi constant	π = 3.141592654... is the ratio between the circumference and diameter of a circle	c = π⋅d = 2⋅π⋅r

Linear Algebra Symbols

Symbol	Symbol Name	Meaning / definition	Example
·	dot	scalar product	a · b
×	cross	vector product	a × b
A⊗B	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
AT	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