When both factors are vectors (so the product is of the form u.v), mathematica assumes them to be in the orientations that make their matrix product the dot product as given by Eq. (4.19). That is, mathematica treats u as a row vector and v as a column vector. This choice correspo...
There's already adotforsympy.matrices.dense.MutableDenseMatrix, but everything is a matrix (rank = 2): vectors are treated as(n, 1)matrix. importsympyfromsympy.abcimportx,y,zdefdot(A,B):A=sympy.sympify(A)B=sympy.sympify(B)rankA=A.rank()C=sympy.tensorproduct(A,B)returnsympy.tensorco...
For the L2-normalized hyper-vectors of the documents, the cosine similarity will be simplified to the form of the inner product of the vectors. Thus, the highly parallel VMM in the DPE makes it a constant time level to calculate the similarities of the input vector and the stored matrix [...
摘要: In this article, the convergence of the sequence a+a+⋯+a 3 3 3 ︸ n is proved, and some inequalities involving this sequence are established for a>0. As by-product, two identities involving irrational numbers are obtained. Two open problems are proposed....
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The position basis representation of ℋ̂H^ was obtained by summing matrix representations of energy terms. The eigenvalues and eigenstates were obtained from the ℋ̂H^ by using Mathematica (Wolfram Research, Champaign, IL, USA) as a calculation tool. The total energies were obtained by ...