Applications where rank-1 matrices are useful

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I am trying to list down applications where having a rank-1 matrix is advantageous. I know only of 2D convolution which boils down to a series of 1D convolutions if filter response is separable.

Can members add any other application here?

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The Spectral Theorem is about decomposing a matrix as a linear combination of rank-one orthogonal projections.

Diagonalization is about decomposing a matrix as a linear combination of rank-one idempotents.