Algebra Symbols

Algebra Symbols – Learning algebra starts with understanding the different symbols used in this type of math. Let’s take a look at common algebra symbols.

Symbol	Symbol Name	Meaning / definition	Example
x	x variable	unknown value to find	when 2x = 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 = 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 = 0.527721566…
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
	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	rank(U) = 3