text>The Kronecker product of two Schur functions s(lambda) and s(mu), denoted s(lambda) * s(mu), is defined as the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group indexed by partitions of n, lambda and mu, respectively. The ...
Therefore, the efficiency and scalability of traditional spectral clustering methods can not be guaranteed for large scale datasets. In this paper, we propose a subspace clustering model based on the Kronecker product. Due to the property that the Kronecker product of a block diagonal matrix with ...
The map H↦BHA′ is the vector-space definition of the Kronecker product of A and B. The transition from differentials to derivatives leads to the need to write down the matrix of the linear map H↦BHA′; this matrix is the usual Kronecker product A⊗B and its properties follow ...
Background What kind of neural computation is actually performed by the primary visual cortex and how is this represented mathematically at the system level? It is an important problem in the visual information processing, but has not been well answered. In this paper, according to our understandi...
Schur complements and matrix inequalities in the Löwner ordering The purpose of this paper is to present a matrix inequality on the Kronecker product that unifies the proofs of many existing matrix inequalities in the L... F Zhang - 《Linear Algebra & Its Applications》 被引量: 43发表: 20...
Based on the Kronecker product of the successive lower order Jacket matrices and the basis matrix, the fast algorithms for realizing these transforms are obtained. Due to the simple inverse and fast algorithms of Arikan polar binary and Alamouti multiple-input multiple-output (MIMO) non-binary ...
To compute the Kronecker product, we define \(P=P(Q)\) as the set of all possible sign permutations of Q terms. For example, for \(Q = 3\) we have $$\begin{aligned} P(3) = \{\{+,+,+\},\{+,+,-\},\{+,-,-\},\cdots ,\{-,-,-\}\}. \end{aligned}$$ (23) ...
The definition of convergence of an infinite product of scalars is extended to the infinite usual and Kronecker products of matrices. The new definitions are less restricted invertibly convergence. Whereas the invertibly convergence is based on the invertible of matrices; in this study, we assume...
The Kronecker product structure is utilized to establish orthogonal factorial structure for the class of designs and to identify a Principle of Generalized Interaction.doi:10.1080/03610928608829183VossD.T.Marcel Dekker, Inc.Communication in Statistics- Theory and MethodsD. Voss, On generalizations of the...
where \(\otimes \) denotes the Kronecker product of matrices (Gantmacher, 1959; Horn & Johnson, 2013). In our paper instead of \(\mathbb {R}^n\) we admit an arbitrary separable Hilbert space \({\mathcal {H}}.\) This requires a non-trivial Schechter’s result on the spectrum of ...