Maths for ML / Notation

\boldsymbol{\Sigma} = \operatorname{Cov}(\mathbf{x})

covariance matrix

Probability and statisticsIntermediate

Say it “Sigma / covariance of x”

Matrix whose entries say how pairs of features vary together. Same symbol as sum — context (bold, no limits) tells you which.

Example

\boldsymbol{\Sigma}_{ij} = \operatorname{Cov}(x_i, x_j)

In code

np.cov(X, rowvar=False)

torch.cov(X.T)

Where you’ll see it in ML

PCA, multivariate Gaussians, whitening.

Don’t confuse it with

$\sum_{i=1}^{n} x_i$ summation Add up the expression for each value of the index — it's a for-loop that accumulates.
$\sigma,\ \sigma^2,\ \sigma(z)$ sigma Lowercase σ is the standard deviation (σ² the variance) — or, as a function σ(z), the sigmoid. Capital Σ is a sum or a covariance matrix.
$\operatorname{Var}(X)$ variance Average squared distance from the mean — how spread out a variable is.

Lessons that use it

PCA: the directions where the data varies most

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