CS168: The Modern Algorithmic Toolbox Lecture #10: Tensors, and Low-Rank Tensor Recovery
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چکیده
Definition 1.1 A n1× n2× . . .× nk k-tensor is a set of n1 · n2 · . . . · nk numbers, which one interprets as being arranged in a k-dimensional hypercube. Given such a k-tensor, A, we can refer to a specific element via Ai1,i2,...,ik . A 2-tensor is simply a matrix, with Ai,j referring to the i, jth entry. You should think of a n1×n2×n3 3-tensor as simply a stack of n3 matrices, where each matrix has size n1×n2. The entry Ai,j,k of such a 3-tensor will refer to the i, jth entry of the kth matrix in the stack.
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