Commonly used math symbols in machine learning texts.


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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


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


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}


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