Sentence examples for sum of matrices from inspiring English sources

A ⊕ B ≜ diag ( A, B ) is the direct sum of matrices [30].

where I m-6 is the identity matrix of size m - 6, m is the dimension of x,⊕ denotes the direct sum of matrices, Π is a permutation matrix fulfilling Π [ …, x a, …, x b, … ] = [ x a, x b, … ]. and z 1 = D γ (x a - x b ).

They showed that for many applications, a naive unweighted sum of matrices is sufficient unless multiple noisy data sets are among the available data sets, and that optimization of the weights is only beneficial when sufficient data are available to more reliably estimate the weights.

The direct product and direct sum of matrices are indicated by ⊗ and ⊕, respectively.

In fact, in this case, (L_{mathbb {K}}(E)) is a finite direct sum of matrix algebras over (mathbb {K}) (cf., [2, Theorem 3.1]).

Figure 1 Matrix estimation errors, with a random tensor of size 8 × 8 × 8 and rank 5. (a) Matrix A. (b) Matrix B. (c) Matrix S. Figure 2 Sum of matrix estimation errors, with a random tensor of size 3 × 3 × 3 and rank 5. Note the asymptote depending on the maximum number of iterations executed.

A variety of methods exist to decompose a mathematical matrix into a sum of simpler matrices that are in some sense orthogonal or independent of one another [15].

Special attention is paid to the star ordering of a sum of two matrices and the minus ordering of matrix product.

The formula of Wilks' Λ is given as (2) Λ = Π 1 (1 + λ k ), where λ k 's are the eigenvalues of the matrix S  (= E−1 H), and E is within sum of squares matrix (sample covariance matrix) and H is between sum of squares matrix.

In this paper, we consider the problem of decomposing an integer matrix into a weighted sum of binary matrices that have the strict consecutive ones property.

Other complex models like Tamura-Nei [ 21] do not even permit the decomposition of its transition matrix into the convex sum of permutation matrices.