List of mathematical algebra symbols and signs.
Algebra math symbols table
Symbol | Symbol Name | Meaning / definition | Example |
---|---|---|---|
x | x variable | unknown value to find | when 2x = 4, then x = 2 |
= | equals sign | equality | 5 = 2+3 5 is equal to 2+3 |
≠ | not equal sign | inequality | 5 ≠ 4 5 is not equal to 4 |
≡ | 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 | y ∝ x when y = kx, k constant |
∞ | 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 | | vertical bars | 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 = 0.5772156649... | |
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 | dim(U) = 3 |
Algebra is a subfield of mathematics pertaining to the manipulation of symbols and their governing rules. The following is a compilation of symbols from the different branches of algebra, which include basic algebra, number theory, linear algebra and abstract algebra.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for expressing all mathematics.
The most basic symbols are the decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the letters of the Latin alphabet. The decimal digits are used for representing numbers through the Hindu–Arabic numeral system. Historically, upper-case letters were used for representing points in geometry, and lower-case letters were used for variables and constants. Letters are used for representing many other sort of mathematical objects. As the number of these sorts has dramatically increased in modern mathematics, the Greek alphabet and some Hebrew letters are also used. In mathematical formulas, the standard typeface is italic type for Latin letters and lower-case Greek letters, and upright type for upper case Greek letters. For having more symbols, other typefaces are also used, mainly boldface script typeface (the lower-case script face is rarely used because of the possible confusion with the standard face), German fraktur and blackboard bold (the other letters are rarely used in this face, or their use is unconventional).
The use of Latin and Greek letters as symbols for denoting mathematical objects is not described in this article. For such uses, see Variable (mathematics) and List of mathematical constants. However, some symbols that are described here have the same shape as the letter from which they are derived, such as and .
Letters are not sufficient for the needs of mathematicians, and many other symbols are used. Some take their origin in punctuation marks and diacritics traditionally used in typography. Other, such as + and =, have been specially designed for mathematics, often by deforming some letters, as in the cases of and .
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