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 | a ≤ x ≤ b} x∈ [2,6] delta change / difference ∆t = t_{1 }– t_{0} discriminant Δ = b^{2} – 4ac sigma summation – sum of all values in range of series ∑ x_{i}= x_{1}+x_{2}+…+x_{n} sigma double summation capital pi product – product of all values in range of series ∏ x_{i}=x_{1}∙x_{2}∙…∙x_{n} 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)
(f ∘g)
(a,b)
[a,b]
∆
∆
∑
∑∑
∏
e
γ
φ
π
Symbol |
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x |
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 | |
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 |