Notice that this last equation is vector valued; the left hand side is the zero element in \ mathbb { R } ^ { 3 }.
42.
Obviously, A x is ill-defined if \ Delta ^ 2 x contains a zero element, or equivalently, if the sequence of first differences has a repeating term.
43.
Given a non-zero element \ varphi of " H * ", the orthogonal complement of the kernel of \ varphi is a one-dimensional subspace of " H ".
44.
In this case any two non-zero elements of " L " and " U " matrices are parameters of the solution and can be set arbitrarily to any non-zero value.
45.
The latter can be easily done by taking, for all nonzero elements of the quotient ring, a sequence starting from a point beyond the last zero element of the sequence.
46.
We also see that augmentation of each codeword of \ mathit { E _ c } by adding a leading zero element produces a vector which satisfies Property " U ".
47.
One property of the NAF is that we are guaranteed that every non-zero element \ scriptstyle d _ i is followed by at least \ scriptstyle w \,-\, 1 additional zeroes.
48.
All in all, when the non-zero elements of the measurement matrix are chosen form a continuous distribution then the SBB and XH algorithm that use ECN rule can be implemented efficiently.
49.
Since Genie only wants to find the value of the non-zero elements of the signal it is not necessary to employ rules that are responsible for zero valued variable node in this algorithm.
50.
The inverse of a non zero element of is the coefficient in B�zout's identity, which may be computed by extended GCD algorithm . ( the GCD is 1 because the minimal polynomial is irreducible ).
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