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We begin with partitioned (i.e., block) matrices and the elementary operations on the partitioned matrices. We discuss the determinants and present explicit forms of the inverses of 2 × 2 block matrices. We study the ranks of sum A+B and product AB of matrices A and B (of appropriate sizes).

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Partitioned Matrices, Ranks, and Eigenvalues

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  • 发表日期：

    2026年

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  • Fuzhen Zhang

摘要

We begin with partitioned (i.e., block) matrices and the elementary operations on the partitioned matrices. We discuss the determinants and present explicit forms of the inverses of 2 × 2 block matrices. We study the ranks of sum A+B and product AB of matrices A and B (of appropriate sizes).