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 = 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 | 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 | |
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 |