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Algebra Symbols
Algebra is a branch of mathematics that deals with symbols and the rules that govern their use. These symbols are known as variables in algebra because they represent quantities with no set values. Equations in mathematics explain relationships between variables in the same way that sentences indicate relationships between specific words. It is critical to understanding the important mathematical symbols and terminology used in algebra.
Symbols in Algebra and their Names
Let's look at the names of some popular algebra symbols that are used in both basic and advanced algebra.
| Algebraic Symbol | Name | Definition of the symbol | Example (if necessary) |
| x | x variable | unknown value to find | when 3 x = 6, then x = 2 |
| := | equal by definition | equal by definition | |
| ≈ | approximately equal | approximation | sin (0.02) ≈ 0.02 |
| ∝ | proportional to | proportional to | y ∝ x when y = ax, a constant |
| ~ | approximately equal | weak approximation | 10.2 ~ 10 |
| ≜ | equal by definition | equal by definition | |
| [ ] | brackets | calculate expression inside first | [(1+3)*(1+4)] = 20 |
| ≫ | much greater than | much greater than | 500000 ≫ 1 |
| ( ) | parentheses | calculate expression inside first | 2 * (3+4) = 14 |
| ⌊ x ⌋ | floor brackets | rounds number to lower integer | ⌊3.2⌋= 3 |
| ∞ | lemniscate | infinity symbol | |
| ≡ | equivalence | identical to | |
| | x | | single vertical bar | absolute value | | -9 | = 9 |
| ≪ | much less than | much less than | 1 ≪ 8000000 |
| { } | braces | set | |
| ⌈ x ⌉ | ceiling brackets | rounds number to upper integer | ⌈4.1⌉= 5 |
| f ( x ) | function of x | maps values of x to f(x) | f ( x ) = 7x +8 |
| ( f ∘ g ) | function composition | ( f ∘ g ) ( x ) = f ( g ( x )) | f ( x )=8 x , g ( x )= x-4 ⇒( f ∘ g )( x )=8( x -4) |
| ( a , b ) | open interval | ( a , b ) = { x | a < x < b } | x ∈ (1,5) |
| [ a , b ] | closed interval | [ a , b ] = { x | a ≤ x ≤ b } | x ∈ [0,5] |
| ∆ | delta | change / difference | ∆ t = t 1 – t 0 |
| ∑ | sigma | summation – sum 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 → ∞ |
| ∆ | discriminant | Δ = b 2 – 4 ac | |
| ∏ | capital pi | product – product of all values in range of series | ∏ x i =x 1 ∙x 2 ∙…∙x n |
| π | pi constant | π = 3.141592654… is the ratio between the circumference and diameter of a circle | c = π · d = 2· π · r |
| ∑∑ | sigma | double summation | ∑ 2 j = 1 ∑ 8 i = 1 x i , j = ∑ 8 i = 1 x i , j + ∑ 8 i = 1 x i , 2 |
| γ | Euler-Mascheroni constant | γ = 0.527721566… | |
| φ | golden ratio | golden ratio constant | |
| Symbol | Symbol Name | Meaning/definition | Example |
| A -1 | inverse matrix | A A -1 = I | |
| × | cross | vector product | a × b |
| ⟨ x , y ⟩ < | inner product | ||
| rank( A ) | matrix rank | rank of matrix A | rank( A ) = 4 |
| ∙ | dot | scalar product | a ∙ b |
| det(A) | determinant | determinant of matrix A | |
| [ ] | brackets | matrix of numbers | |
| ( ) | parentheses | matrix of numbers | |
| A ⊗ B | tensor product | tensor product of A and B | A ⊗ B |
| A T | transpose | matrix transpose | (AT)ij = (A)ji |
| A † | Hermitian matrix | matrix conjugate transpose | (A†) ij = (A) ji |
| | A | | determinant | determinant of matrix A | |
| || x || | double vertical bars | norm | |
| dim(U) | dimension | dimension of matrix A | rank(U) = 5 |
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