Outer product

Linear algebra · Formula · Not yet linked from a lesson

(uv⊤)ij=uivj(\mathbf{u} \mathbf{v}^{\top})_{ij} = u_i v_j

Takes two vectors and produces a full matrix, every element of one multiplied by every element of the other. The result always has rank one, which is the idea low-rank adapters are built on.

Symbols

u\mathbf{u}
A column vector of length m.
v\mathbf{v}
A column vector of length n.
⊤\top
Transpose, turning a column into a row.
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