Algebra symbols list

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

≡ 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 = t₁- t₀

∆ discriminant Δ = b² - 4ac

∑ sigma summation - sum of all values in range of series ∑ x_i= x₁+x₂+...+x_n

∑∑ sigma double summation

∏ capital pi product - product of all values in range of series ∏ x_i=x₁∙x₂∙...∙x_n

e e 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 × b

A⊗B tensor product tensor product of A and B A ⊗ B

$\langle x,y \rangle$ 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
(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
rank(U) = 3

Statistical symbols ►

See also

Math symbols

Basic math symbols

Statistical symbols

Set symbols

Calculus symbols

Infinity symbol

Symbol	Symbol Name	Meaning / definition	Example
x	x variable	unknown value to find	when 2x = 4, then x = 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! = 123*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 = t₁- t₀
∆	discriminant	Δ = b² - 4ac
∑	sigma	summation - sum of all values in range of series	∑ x_i= x₁+x₂+...+x_n
∑∑	sigma	double summation
∏	capital pi	product - product of all values in range of series	∏ x_i=x₁∙x₂∙...∙x_n
e	e 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

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
$\langle x,y \rangle$	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	(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	rank(U) = 3

Algebra Symbols

Algebra math symbols table

Linear Algebra Symbols

See also

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