Rank of a Hadamard product

Hadamard Powers and Kernel Perceptrons

“…If the rank is maximal, then any separation of the data set can be classified by a polynomial kernel perceptron of the corresponding degree. In this context we provide a new proof for the fact that any Boolean function in n variables can be realized by a kernel perceptron with polynomial kernel of degree n. We compare our rank calculations to lower bounds obtained quite recently in [1]. Moreover, we show that generically the rank of the d-th Hadamard power of a matrix A ∈ R n×m is min rank…”

“…A prominent result is Schur's product theorem [9], which states that the Hadamard product preserves definiteness. Definiteness, rank, and other properties of Hadamard powers have been discussed in [10,11,12,13,14,15,1,16,17]. Applications of Hadamard products in artificial intelligence can be found in [18].…”

Local Calibration of a Weak Stiffness On-Machine Measuring Device with a New 3-D Calibrator

“…On the other hand, the averaged accuracy improvement of the OMM device is limited (not more than one order of magnitude) in this paper, so, the accuracy and stability of the 3-D ball array calibrator are still worth further improvement in future studies. 1,2,3,27,51,20,21,22,23,26,71,72,24,25,48,49,50,68,69,70,4,5,6,71,7,31,55,28,29,30,52,53,54,8,9,10,67,73,11,35,59,12,13,14,15,34,63,74,32,33,56,   , 57, 58, 60, 61, 62, 64, 65, 66 0, 1, 2, 3, 6, 7, 8, 9, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25...…”

“…).coef 1 xy    . The operator "" o is Hadamard product [34] . The algorithm scans matrix row by row and column by column, and performs the…”

Special Real and Dual Matrices with Hadamard Product

“…In the literature, there are more than 400 scientific papers using Hadamard product about positive semidefinite matrix, upper bound for an arbitrary determinant with the help of Hadamard matrix product written by Jacques Hadamard. Issai Schur does not seem to know of any previous work on the product (1.1), which shows that as long as A and B are positive semi-definite, their product hadamard is also positive [2][3][4]. Hence, some mathematicians used the name Hadamard and the others used Schur product.…”