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Complexity Theorems - Theorem 1.
Complexity Theorems – Theorem 1.
Anything that can be called theory – a theory is something that can be verified empirically in a laboratory – usually has some characteristic constant, a metric, an equation, or some theorems. Think of the theory of gravity, or the theory of relativity. “Theory” means “Explanation for an observable fact, which has been extensively tested, fits all the known observations and can be used to predict…
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ECE1254H Modeling of Multiphysics Systems. Lecture 6: Singular value decomposition, and conditioning number. Taught by Prof. Piero Triverio
ECE1254H Modeling of Multiphysics Systems. Lecture 6: Singular value decomposition, and conditioning number. Taught by Prof. Piero Triverio
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Disclaimer
Peeter’s lecture notes from class. These may be incoherent and rough.
Matrix norm
We’ve defined the matrix norm of \( M \), for the system \( \overline{{y}} = M \overline{{x}} \) as
\begin{equation}\label{eqn:multiphysicsL6:21} \Norm{M} = \max_{\Norm{\overline{{x}}} = 1} \Norm{ M \overline{{x}} }. \end{equation}
We…
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