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The determinant is a map that assigns to every square matrix \(A\in R^{n,n}\) , where R is a commutative ring with unit, an element of R. This map has very interesting and important properties. For instance it yields a necessary and sufficient condition for the invertibility of \(A\in R^{n,n}\) . Moreover, it forms the basis for the definition of the characteristic polynomial of a matrix in Chapter 8 .

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Determinants of Matrices

  • 章节

  • 发表日期：

    2025年

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  • Jörg Liesen,
  • Volker Mehrmann

摘要

The determinant is a map that assigns to every square matrix \(A\in R^{n,n}\) , where R is a commutative ring with unit, an element of R. This map has very interesting and important properties. For instance it yields a necessary and sufficient condition for the invertibility of \(A\in R^{n,n}\) . Moreover, it forms the basis for the definition of the characteristic polynomial of a matrix in Chapter 8 .