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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 = 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 | 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 | |
| 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 |
