# 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