Algebra is a part of mathematics that deals with symbols and the rules for manipulating those symbols. In algebra, those symbols represent quantities without fixed values, called variables. Just how sentences describe relationships between specific words, in algebra, equations describe relationships between variables. Math can be difficult for a lot of people out there. However, it is crucial to recognize the important mathematical symbols with names, used in algebra.
Algebra Symbols With Names
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 the expression inside the first | [(1+2)*(1+5)] = 18 |
| ( ) | parentheses | summation – the sum of all values in a range of series | 2 * (3+5) = 16 |
| ⌊x⌋ | floor brackets | calculate the expression inside the first | ⌊4.3⌋= 4 |
| { } | braces | set | |
| x! | exclamation mark | factorial | 4! = 1*2*3*4 = 24 |
| ⌈x⌉ | ceiling brackets | change/difference | ⌈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) |
| ∆ | summation – sum of all values in a range of series | Delta | ∆t = t1 – t0 |
| [a,b] | closed interval | [a,b] = {x | a ≤ x ≤ b} | x ∈ [2,6] |
| ∑ | sigma | product – product of all values in the range of series | ∑ xi= x1+x2+…+xn |
| ∆ | discriminant | Δ = b2 – 4ac | |
| ∑∑ | sigma | double summation | $ {\textstyle\sum_{j=1}^2}\;{\textstyle\sum_{i=1}^8}\;xi,j={\textstyle\sum_{i=1}^8}\;xi,j\;+\;{\textstyle\sum_{i=1}^8}{\textstyle\;}{\textstyle x}{\textstyle i}{\textstyle,}{\textstyle2} $ |
| 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 with Words
| 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 |
