A recurrent neural network computing the largest imaginary or real part of eigenvalues of real matrices

A recurrent neural network computing the largest imaginary or real part of eigenvalues of real matrices

As the efficient calculation of eigenpairs of a matrix, especially, a general real matrix, is significant in engineering, and neural networks run asynchronously and can achieve high performance in calculation, this paper introduces a recurrent neural network (RNN) to extract some eigenpair. The RNN, whose connection weights are dependent upon the matrix, can be transformed into a complex differ...

A Complex Neural Network Algorithm for Computing the Largest Real Part Eigenvalue and the corresponding Eigenvector of a Real Matrix

A concise functional neural network computing the largest modulus eigenvalues and their corresponding eigenvectors of a real skew matrix

Quick extraction of the largest modulus eigenvalues of a real antisymmetric matrix is important for some engineering applications. As neural network runs in concurrent and asynchronous manner in essence, using it to complete this calculation can achieve high speed. This paper introduces a concise functional neural network (FNN), which can be equivalently transformed into a complex differential ...

A real explanation for imaginary eigenvalues

Abstract This paper first reviews how anti-symmetric matrices in two dimensions yield imaginary eigenvalues and complex eigenvectors. It is shown how this carries on to rotations by means of the Cayley transformation. Then the necessary tools from real geometric algebra are introduced and a real geometric interpretation is given to the eigenvalues and eigenvectors. The latter are seen to be two...

Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices

This paper introduces a novel neural-network-based approach for extracting some eigenpairs of real normal matrices of order n. Based on the proposed algorithm, the eigenvalues that have the largest and smallest modulus, real parts, or absolute values of imaginary parts can be extracted, respectively, aswell as the corresponding eigenvectors. Although the ordinary differential equation on which ...