Sentence examples for matrix are nonnegative from inspiring English sources

Because the entries of matrix are nonnegative, we further define.

Therefore, the two loading matrices of the three-way array, which are equal to the mixing matrix, are nonnegative.

It is necessary and sufficient for a positive semidefinite matrix that all the principal minor determinants of the matrix are nonnegative real numbers.

It is necessary and sufficient for a negative semidefinite matrix that all the odd order principal minor determinants of the matrix are non-positive real numbers and all the even order principal minor determinants of the matrix are nonnegative real numbers.

The vector and the matrix is nonnegative if and,, respectively.

Meyer [1] introduced the concept of the Perron complement, obtained the Perron complement of a nonnegative irreducible matrix is nonnegative irreducible, and first used the closure property of a nonnegative irreducible matrix to construct a divided and conquer algorithm to compute the Perron vector for a Markov chain.

But the matrices are nonnegative in the above inequality, thus (5.8).

However, the implication discussed above may be lost if (4.15) is not satisfied, even if the matrices are nonnegative, as the following example shows.

All eigenvalues of the matrix W are nonnegative, thus the guided filter kernel matrix is positive definite matrix.

For A ∈ ℝ n × m, we write A ≽ 0 ≼ 0, ≻ 0, and ≺ 0 to indicate that all elements of matrix A are nonnegative (non-positive, positive, and negative) and the notation of matrices will be used throughout this brief: A = [a lg ] and A i = [ a l g ( i ) ] ⋅.

From formula of solution representation (1.3), it is clear that property (1.4) (1.5) is true if all elements of the matrices and are nonnegative.