# Algebra Symbols

## Math Algebra Symbols

Symbol Name Meaning / definition Example 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 floor brackets rounds number to lower integer 4.3= 4 ceiling brackets rounds number to upper integer 4.3= 5 exclamation mark factorial 4! = 1*2*3*4 = 24 single vertical bar absolute value | -5 | = 5 function of x maps values of x to f(x) f (x) = 3x+5 function composition

(f g)(x) = f (g(x))

f (x)=3x, g(x)=x-1 (f g)(x)=3(x-1) open interval (a,b) = {x | a < x < b} x (2,6) 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 capital pi product – product of all values in range of series ∏ xi=x1∙x2∙…∙xn e constant / Euler’s number e = 2.718281828… e = lim (1+1/x)x , x→∞ Euler-Mascheroni constant γ = 0.527721566… golden ratio golden ratio constant pi constant π= 3.141592654…

is the ratio between the circumference and diameter of a circle

c = π·d = 2·π·r

:=
~

( )
[ ]
{ }
x
x
x!
| x |
f (x)
(fg)
(a,b)
[a,b]

∑∑

e
γ
φ
π

Symbol
x

## 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
[ ] 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

rank(U) = 3