Hadamard product

The Hadamard product multiplies corresponding entries of two vectors or matrices of the same shape, without summing across entries.

Elementwise operation: An operation that acts separately on corresponding entries of arrays. The Hadamard product is the standard entry-by-entry multiplication of arrays.
Array shape: The sizes of an array along each of its dimensions. Both operands must have matching shapes for the ordinary Hadamard product.
Gating (neural networks): A neural-network mechanism that modulates one signal by another, often through elementwise multiplication. Gates use Hadamard products to select or scale features and activations.
Dot product: A scalar formed by multiplying corresponding vector components and summing the products. The Hadamard product stops before the summation that defines a dot product.
Matrix multiplication: An operation that combines rows of one matrix with columns of another through dot products. Unlike matrix multiplication, it multiplies matching entries and does not sum products.
Index notation: A notation that expresses mathematical objects and operations using indexed components. The rule is stated directly as multiplying entries with identical indices.
Dropout (neural networks): A training technique that randomly suppresses neural-network activations to reduce overfitting. A binary mask is multiplied elementwise with activations during dropout.
Outer product: A matrix formed by multiplying every component of one vector by every component of another. It combines all cross-pairs and changes shape instead of matching corresponding entries.
Kronecker product: A matrix operation that forms a block matrix from all pairwise products of entries. It expands dimensions, whereas the Hadamard product preserves the shared shape.
Vector: An ordered collection of components that can represent a direction or a list of values. For vectors, the Hadamard product multiplies components position by position.

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