Titlebook: Eigenvalue Problem and Nonlinear Programming Problem; For Economic Studies Keiko Nakayama Book 2024 Springer Nature Singapore Pte Ltd. 2024

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,Frobenius’ Theorem,This chapter focuses on the Frobenius theorem, which plays a major role in economics. This chapter, explicitly states Frobenius theorem when extended to nonlinear transformations though it is often treated only in terms of linear transformations.

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Dominant Diagonal Matrix and the Quadratic Form,This chapter, first defines the dominant diagonal matrix and discusses the basic properties of this (Hadamard’s theorem and its extensions). Then, this chapter describes the properties of quadratic form or Hermitian matrices. Moreover, based on these arguments, some theorems on the stability of matrices are proved.

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978-981-99-2945-0Springer Nature Singapore Pte Ltd. 2024

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