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I came across this statement:

When a d-dimensional kernel can be expressed as he outer product of d vectors, one vector per dimension, the kernel is called separable.

With kernel being kernel in convolution, function g: $$f(x) = \int h(u)g(x-u)du$$ My question is, what are conditions that kernel can be expressed as outer product? I got familiar with what outer product is, but I can't find conditions. Does anyone know name of related theorem?

econ
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1 Answers1

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Eigenvalues can give you some hint. However, a More direct method is to treat the 2D kernel as a 2D matrix K and to take its singular value decomposition (SVD). If only the first singular value is non-zero, the kernel is separable.

Ankit Swarnkar
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