Notation

Commonly used math symbols in machine learning texts. Check more on the referenced sites 1 2.

Note

Use the table generator to quickly add new symbols. Import current tables into tablesgenerator from figures/*.tgn. Export and save your changes. Also see helpful multiline editing in Sublime.

Algebra

Symbol

Name

Description

Example

\((f ∘ g)\)

composite function

a nested function

(f ∘ g)(x) = f(g(x))

\(∆\)

delta

change / difference

∆x = x_1 - x_0

\(e\)

Euler’s number

e = 2.718281828

s = frac{1}{1+e^{-z}}

\(\sum\)

summation

sum of all values

∑ x_i = x_1 + x_2 + x_3

\(\prod\)

capital pi

product of all values

∏ x_i = x_1∙x_2∙x_3

\(\epsilon\)

epsilon

tiny number near 0

lr = 1e-4

Calculus

Symbol

Name

Description

Example

\(x'\)

derivative

first derivative

(x^2)’ = 2x

\(x''\)

second derivative

second derivative

(x^2)’’ = 2

\(\lim\)

limit

function value as x approaches 0

\(∇\)

nabla

gradient

∇f(a,b,c)

Linear algebra

Symbol

Name

Description

Example

\([ ]\)

brackets

matrix or vector

\(M = [1 3 5]\)

\(\cdot\)

dot

dot product

\((Z = X \cdot W\)

\(\odot\)

hadamard

hadamard product

\(A = B \odot C\)

\(X^T\)

transpose

matrix transpose

\(W^T \cdot X\)

\(\vec x\)

vector

vector

\(v = [1 2 3]\)

\(X\)

matrix

capitalized variables are matrices

\(X, W, B\)

\(\hat x\)

unit vector

vector of magnitude 1

\(\hat x = [0.2 0.5 0.3]\)

Probability

Symbol

Name

Description

Example

\(P(A)\)

probability

probability of event A

P(x=1) = 0.5

Set theory

Symbol

Name

Description

Example

\({ }\)

set

list of distinct elements

S = {1, 5, 7, 9}

Statistics

Symbol

Name

Description

Example

\(μ\)

population mean

mean of population values

\(\bar x\)

sample mean

mean of subset of population

\(σ^2\)

population variance

variance of population value

\(s^2\)

sample variance

variance of subset of population

\(σ_X\)

standard deviation

population standard deviation

\(s\)

sample std dev

standard deviation of sample

\(ρX\)

correlation

correlation of variables X and Y

\(\tilde x\)

median

median value of variable x

References

1

http://www.tablesgenerator.com/text_tables

2

http://www.rapidtables.com/math/symbols/Basic_Math_Symbols.html