Notation

Commonly used math symbols in machine learning texts.

Note

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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.htm