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picatepica
searching PlanetScale…
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by
picatepica
3y ago
You are right, A can be non-square because A and AA^t both have the same number of rows. To prove that A and AA^t have the same range you apply that if AA^T v = 0 then v^TAA^Tv = 0, this implies that (A^Tv)^T (A^tv) = 0, so that A^Tv = 0
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by
picatepica
3y ago
> In linear algebra the column space of a matrix is the same as the column space of the product with itself transposed: C(A) = C(AA^T). I think you need A to be a square matrix since AA^T is a square matrix. So the result is no true in