Maths for ML / Notation

A \times B

Cartesian product

SetsIntermediate

Say it “A cross B”

All ordered pairs with the first from A and the second from B.

Example

\mathcal{X} \times \mathcal{Y}

All possible (input, label) pairs.

In code

itertools.product(A, B)

Where you’ll see it in ML

A dataset is a sample from 𝒳 × 𝒴. Also why matrix shapes are written m × n.

Don’t confuse it with

$a \times b$ times / dimension Ordinary multiplication — or, between sizes, 'by' as in a 3 × 4 matrix.
$\mathbf{a}\times\mathbf{b}$ cross product (3-D) For two 3-D vectors, gives a vector perpendicular to both.

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