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