Eigenvalue

  • (noun): (mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinant.

Some articles on eigenvalues, eigenvalue:

Matrix Differential Equation - Solved Example of A Matrix ODE - Second Step
... For each of the eigenvalues calculated we are going to have an individual eigenvector ... For our first eigenvalue, which is, we have the following Simplifying the above expression by applying basic matrix multiplication rules we have ... Doing so produces a very simple vector, which is the required eigenvector for this particular eigenvalue ...
Segmentation-based Object Categorization - Segmentation Using Normalized Cuts - The Ncut Algorithm
... problem can be solved by solving the generalized eigenvalue problem for the second smallest generalized eigenvalue ... Solve for eigenvectors with the smallest eigenvalues ... Use the eigenvector with the smallest eigenvalue to bipartition the graph (e.g ...
Mathematical Description - Spatial Correlation Matrices
... spatial correlation depends directly on the eigenvalue distributions of the correlation matrices and ... represents a spatial direction of the channel and its corresponding eigenvalue describes the average channel/signal gain in this direction ... High spatial correlation is represented by large eigenvalue spread in or, meaning that some spatial directions are statistically stronger than others ...
Preconditioner - Preconditioning For Eigenvalue Problems
... Eigenvalue problems can be framed in several alternative ways, each leading to its own preconditioning ... Knowing (approximately) the targeted eigenvalue, one can compute the corresponding eigenvector by solving the related homogeneous linear system, thus allowing to use ... Finally, formulating the eigenvalue problem as optimization of the Rayleigh quotient brings preconditioned optimization techniques to the scene ...
Power Iteration - Analysis
... the first column of is an eigenvector of corresponding to the dominant eigenvalue ... Since the dominant eigenvalue of is unique, the first Jordan block of is the matrix, where is the largest eigenvalue of A in magnitude ... has a nonzero component in the direction of the dominant eigenvalue, so ...