Linear Algebra Symbols

Algebra Symbols

Algebra is a part of mathematics which deals with symbols and the rules for manipulating those symbols. In algebra, those symbols represent quantities without fixed values, called as variables. Just how sentences describe relationships between specific words, in algebra, equations describe relationships between variables. Math can be difficult for allot of people out there. However, it is crucial to recognize that even symbols, used in algebra, have names, and those names are made up of letters and words.
Let’s explore the names of common algebra symbols used in both basic algebra and more advanced levels.

Symbol	Symbol Name	Meaning / definition	Example
≡	equivalence	identical to
x	x variable	unknown value to find	when 2x = 4, then x = 2
:=	equal by definition	equal by definition
≜	equal by definition	equal by definition
≈	approximately equal	approximation	sin(0.01) ≈ 0.01
~	approximately equal	weak approximation	11 ~ 10
∞	lemniscate	infinity symbol
∝	proportional to	proportional to	y ∝ x when y = kx, k constant
≫	much greater than	much greater than	1000000 ≫ 1
≪	much less than	much less than	1 ≪ 1000000
[ ]	brackets	calculate expression inside first	[(1+2)*(1+5)] = 18
( )	parentheses	calculate expression inside first	2 * (3+5) = 16
⌊x⌋	floor brackets	rounds number to lower integer	⌊4.3⌋= 4
{ }	braces	set
x!	exclamation mark	factorial	4! = 1*2*3*4 = 24
⌈x⌉	ceiling brackets	rounds number to upper integer	⌈4.3⌉= 5
f (x)	function of x	maps values of x to f(x)	f (x) = 3x+5
| x |	single vertical bar	absolute value	| -5 | = 5
(a,b)	open interval	(a,b) = {x | a < x < b}	x ∈ (2,6)
(f ∘g)	function composition	(f ∘g) (x) = f (g(x))	f (x)=3x, g(x)=x-1 ⇒(f ∘g)(x)=3(x-1)
∆	delta	change / difference	∆t = t1 – t0
[a,b]	closed interval	[a,b] = {x | a ≤ x ≤ b}	x ∈ [2,6]
∑	sigma	summation – sum of all values in range of series	∑ xi= x1+x2+…+xn
∆	discriminant	Δ = b2 – 4ac
∑∑	sigma	double summation	${\sum }_{j=1}^2{\sum }_{i=1}^{8}xi,j={\sum }_{i=1}^{8}xi,j+{\sum }_{i=1}^{8}xi,2$
e	e constant / Euler’s number	e = 2.718281828…	e = lim (1+1/x)x , x→∞
∏	capital pi	product – product of all values in range of series	∏ xi=x1∙x2∙…∙xn
γ	Euler-Mascheroni  constant	γ = 0.527721566…
π	pi constant	π = 3.141592654… is the ratio between the circumference and diameter of a circle	c = π·d = 2·π·r
φ	golden ratio	golden ratio constant

Linear Algebra Symbols

Symbol	Symbol Name	Meaning / definition	Example
×	cross	vector product	a × b
∙	dot	scalar product	a ∙ b
$⟨x,y⟩$	inner product
A⊗B	tensor product	tensor product of A and B	A ⊗ B
[ ]	brackets	matrix of numbers
( )	parentheses	matrix of numbers
det(A)	determinant	determinant of matrix A
| A |	determinant	determinant of matrix A
A T	transpose	matrix transpose	(AT)ij = (A)ji
|| x ||	double vertical bars	norm
A †	Hermitian matrix	matrix conjugate transpose	(A†)ij = (A)ji
A -1	inverse matrix	A A-1 = I
dim(U)	dimension	dimension of matrix A	rank(U) = 3
rank(A)	matrix rank	rank of matrix A	rank(A) = 3