A Schur Method for Low-Rank Matrix Approximation
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Fundamentals of Artificial Neural Networks
Fundamentals of Artificial Neural Networks
Further Results on the Asymptotic Memory Capacity of the Generalized Hopfield Network
Neural Processing Letters
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Bipolar matrices are a special class of matrices, consisting of elements assuming only the values -1 and +1. Such matrices appear in various areas of research, including Artificial Neural Networks. Their simplicity can lead to the direct determination or estimation of their measures and characteristics, based on their dimensions. Here we discuss the matter of the bipolar matrix minimum singular value estimation. The geometric interpretation of singular values is combined with analytical experimental results to reveal some regularity, which shows the potential existence of a closed function, describing the minimum non-zero singular values of all possible bipolar matrices of the same dimensions. This function could give some direct information, which can be used constructively in the estimation of the respective matrix condition or the behaviour of the matrix pseudoinverse elements, among other things. We conclude by posing two questions, as regards the existence of this function and the potential acceleration of the process under which we acquire elements, in order to reveal a curve with the desired characteristics.