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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 | axb} 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 Double Sum Ex
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
AB tensor product tensor product of A and B A
B
Inner Product 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

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