Maths for ML / Notation

\mathbf{a}\odot\mathbf{b}

Hadamard (element-wise) product

Linear algebraIntermediate

Say it “a element-wise times b”

Multiply matching entries and keep them as a vector/matrix — no summing.

Example

[1,2]\odot[3,4]=[3,8]

In code

a * b

a * b

Where you’ll see it in ML

Gates in LSTMs/GRUs, masking, dropout.

Don’t confuse it with

$\mathbf{a}\cdot\mathbf{b}$ dot product Multiply matching entries and add them up. Gives one number that's large when the vectors point the same way.
$\mathbf{a}\otimes\mathbf{b}$ tensor / outer / Kronecker product Combines two vectors into a matrix of all pairwise products (outer product), or two matrices into a bigger block matrix (Kronecker).
$f \circ g$ composition Apply g first, then f to the result: (f∘g)(x) = f(g(x)).

Lessons that use it

Special matrices: diagonal, symmetric, orthogonal, triangular, sparse

← All 94 symbols