Question

In a step of the quadratic sieve, the block Lanczos (“LAHN-tsoash”) algorithm is often used to find an element of this set over a finite field. One of the two possibilities given by the finite-dimensional Fredholm Alternative is that an example of this set is trivial. For nilpotent objects, the dimension (-5[1])of this (10[2])set is equal to the number of Jordan blocks. (10[1])This set and its (-5[1])“co-” or “left” analog are two (10[1])of the “four fundamental” (-5[1])sets for an operator. (10[1])Functionals for which this set includes a set (10[1])A make up the annihilator of A. (10[2])This set consists of elements orthogonal (10[1])to all elements of the row (10[1])space. The (10[1])dimension (10[1])of the (-5[1])domain (10[1])equals the dimension of (10[1])the image plus the dimension of this subspace (10[3])of the (10[1])domain. (10[1])For 10 points, singular matrices have nontrivial examples of what subspace, which consists of the vectors mapped to zero? (10[1])■END■ (10[4])

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