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
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

Algebra is a subfield of mathematics pertaining to the manipulation of symbols and their governing rules. The following is a compilation of symbols from the different branches of algebra, which include basic algebra, number theory, linear algebra and abstract algebra.

A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for expressing all mathematics.

The most basic symbols are the decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the letters of the Latin alphabet. The decimal digits are used for representing numbers through the Hindu–Arabic numeral system. Historically, upper-case letters were used for representing points in geometry, and lower-case letters were used for variables and constants. Letters are used for representing many other sort of mathematical objects. As the number of these sorts has dramatically increased in modern mathematics, the Greek alphabet and some Hebrew letters are also used. In mathematical formulas, the standard typeface is italic type for Latin letters and lower-case Greek letters, and upright type for upper case Greek letters. For having more symbols, other typefaces are also used, mainly boldface  script typeface  (the lower-case script face is rarely used because of the possible confusion with the standard face), German fraktur and blackboard bold (the other letters are rarely used in this face, or their use is unconventional).

The use of Latin and Greek letters as symbols for denoting mathematical objects is not described in this article. For such uses, see Variable (mathematics) and List of mathematical constants. However, some symbols that are described here have the same shape as the letter from which they are derived, such as  and .

Letters are not sufficient for the needs of mathematicians, and many other symbols are used. Some take their origin in punctuation marks and diacritics traditionally used in typography. Other, such as + and =, have been specially designed for mathematics, often by deforming some letters, as in the cases of  and .

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