Nullspaces of Matrices and Their Compounds
نویسندگان
چکیده
We consider compound matrices and exterior products in order to generalize a fundamental relation between the eigenspace of a matrix A corresponding to a simple eigenvalue λ and certain minors of A − λI of order n − 1. By means of the Laplace Expansion Theorem, we show that if the geometric multiplicity of λ is k > 1, then the exterior product of k linearly eigenvectors corresponding to λ is uniquely (up to scalar multiples) determined by certain minors of A− λI of order n− k. Additional results are included on the nullspace of a compound matrix.
منابع مشابه
Characterizations and Classifications of M-Matrlces Using Generalized Nullspaces
Several characterizations of the class of M-matrices as a subclass of the class of Z-matrices are given. These characterizations involve alternating sequences, decompositions, and splittings, and all are related to generalized nullspaces.
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