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Every square matrix A has a determinant \(\det (A)\) . With this characteristic of A, we can provide a crucial invertibility criterion for A: A square matrix A is invertible if and only if \(\det (A) \neq 0\) . This criterion is what makes the determinant so useful: We can use it to calculate the eigenvalues and thus solve the crucial problems in engineering sciences, such as principal axis transformation or singular value decomposition.

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The Determinant

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  • 发表日期：

    2026年

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  • Christian Karpfinger

摘要

Every square matrix A has a determinant \(\det (A)\) . With this characteristic of A, we can provide a crucial invertibility criterion for A: A square matrix A is invertible if and only if \(\det (A) \neq 0\) . This criterion is what makes the determinant so useful: We can use it to calculate the eigenvalues and thus solve the crucial problems in engineering sciences, such as principal axis transformation or singular value decomposition.