Sentence examples for be the null space from inspiring English sources

Let (operatorname{Ker}(A)={x inmathbb{R}^{n}:Ax=0}) be the null space of a matrix A, and denote by (lambda_{min^(A)) the minimal nonzero absolute-value eigenvalue of A and by (lambda_{max}(A)) the maximal one.

Let (operatorname{Ker}(A)={x inmathbb {R}^{n}:Ax=0}) be the null space of matrix A. We also use the subscript notation (x_{S}) to denote a vector that is equal to x on the index set S and zero everywhere else and use the subscript notation (X_{S}) to denote a matrix whose rows are those of the rows of X that are in the set index S and zero everywhere else.

Then there is a unique projection whose range is the range of and whose null space is the null space of, or equivalently,.

M being the null space of the operator (vert Bvert^{2}-Vert AVert ^{2}) is a closed subspace of (mathcal{H} ).

Throughout, for any linear operator S in X, (mathcal{R}(S)) denotes the range of S and (mathcal{K}(S)) is the null space of S.

Statistically, this represents the largest norm among K - (i - 1) norms in M - (i - 1 -dimensional subspace, which is the null space of the subspace spanned by the channel vectors of i - 1 -dimensionalcted usubspaceprevious SUS iterations.

This is because these two existing schemes suppress the OOBE by using two properties independent of each other, which are the null space property and the continuous derivative property.

Since the signature matrix C must be one-to-one, the necessary and sufficient condition is that KerC ∩ {- 1, 0, 1} n = {0} n, where KerC is the null space of C. The authors of [22] have applied Theorem 2 in order to develop a large COW matrix from a smaller one.

The complexity of finding the fitness value is dominated by finding the matrices (mathbf {W}^{n}_{ij}) and matrices (mathbf {E}^{n}_{im1} 44, which are the null space of (mathbf {A}^{n}_{j -i)}) and (mathbf {B}^{n}_{j -i,-1)}), respectively.

A sequence of cyclic code with roots α i e 1, α i e 2, α i e 3, ⋯, α i e n i − k i Open image in new window is the null space of the matrix M i = 1 α i e 1 ( α i e 1 ) 2 ⋯ ( α i e 1 ) n i − 1 1 α i e 2 ( α i e 2 ) 2 ⋯ ( α i e 2 ) n i − 1 ⋮ ⋮ ⋮ ⋱ ⋮ 1 α i e n i − k i ( α i e n i − k i ) 2 ⋯ ( α i e n i − k i ) n i − 1. Open image in new window.

Here, null(J is the null space of J and β is a vector containing arbitrary non-zero values.