Linearisation about an equilibrium and the eigenvalue stability criterion (Q1677): Difference between revisions
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| Property / LaTeX source: \\mathbf{u}'=A\\mathbf{u},\\qquad A=D\\mathbf{f}(\\mathbf{x}^{*});\\qquad \\operatorname{Re}(\\lambda)<0\\ \\text{for all eigenvalues } \\lambda\\ \\Rightarrow\\ \\mathbf{x}^{*}\\ \\text{asymptotically stable} / rank | |||
| Property / instance of | |||
| Property / instance of: mathematical expression / rank | |||
Normal rank | |||
| Property / LaTeX source | |||
\\mathbf{u}'=A\\mathbf{u},\\qquad A=D\\mathbf{f}(\\mathbf{x}^{*});\\qquad \\operatorname{Re}(\\lambda)<0\\ \\text{for all eigenvalues } \\lambda\\ \\Rightarrow\\ \\mathbf{x}^{*}\\ \\text{asymptotically stable} | |||
| Property / LaTeX source: \\mathbf{u}'=A\\mathbf{u},\\qquad A=D\\mathbf{f}(\\mathbf{x}^{*});\\qquad \\operatorname{Re}(\\lambda)<0\\ \\text{for all eigenvalues } \\lambda\\ \\Rightarrow\\ \\mathbf{x}^{*}\\ \\text{asymptotically stable} / rank | |||
Normal rank | |||
Latest revision as of 07:28, 4 September 2026
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Linearisation about an equilibrium and the eigenvalue stability criterion |
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Statements
\\mathbf{u}'=A\\mathbf{u},\\qquad A=D\\mathbf{f}(\\mathbf{x}^{*});\\qquad \\operatorname{Re}(\\lambda)<0\\ \\text{for all eigenvalues } \\lambda\\ \\Rightarrow\\ \\mathbf{x}^{*}\\ \\text{asymptotically stable}
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