15.7k 3 3 gold badges 15 15 silver badges 28 28 bronze badges. If the right hand side matrix D of the matrix product AD is diagonal, the computational load reduces to M. matlab matrix vector multiplication Share. The Diagonal function in the LinearAlgebra package creates a diagonal matrix from a vector of its diagonal elements. Ask Question Asked 7 years, 5 months ago. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. Matlab multiply each row in matrix by different number. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. In MATLAB, the Hadamard product is expressed as dot multiply. Second, we study factored tensors, which have the property that they can be assembled from more basic components. matrix multiplication of the corresponding diagonal matrix of one vector by the other vector. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Use MATLAB to find a matrix Q and a diagonal matrix D such that P QDQ-1. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation.
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