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For every square complex matrix A there is a Jordan normal form J, i.e., there exists an invertible matrix \(B \in {\mathbb C}^{n \times n}\) with \(J = B^{-1} A \, B\) . The columns of B form a corresponding Jordan basis. We obtain such a matrix or Jordan basis B by successively traversing the generalised eigenspaces. The key role is played by the matrices \(N = A - \lambda \, E_n\) for the eigenvalues \(\lambda \) of A.

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The Jordan Normal Form II

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  • 发表日期：

    2026年

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  • Christian Karpfinger

摘要

For every square complex matrix A there is a Jordan normal form J, i.e., there exists an invertible matrix \(B \in {\mathbb C}^{n \times n}\) with \(J = B^{-1} A \, B\) . The columns of B form a corresponding Jordan basis. We obtain such a matrix or Jordan basis B by successively traversing the generalised eigenspaces. The key role is played by the matrices \(N = A - \lambda \, E_n\) for the eigenvalues \(\lambda \) of A.