mvg:lecture_02:start
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| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| mvg:lecture_02:start [2018/11/19 12:33] – [Eigenvalue Problem] admin | mvg:lecture_02:start [2020/02/04 15:12] (current) – [Eigenvalue Problem] admin | ||
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| $A\mathbf{v} = \lambda \mathbf{v}$ | $A\mathbf{v} = \lambda \mathbf{v}$ | ||
| - | $(A-\lambda \unity) A = 0$ | + | $(A-\lambda \one) A = 0$ |
| $\left(A-\lambda \unity \right) A = 0$ | $\left(A-\lambda \unity \right) A = 0$ | ||
| Line 37: | Line 37: | ||
| **Question: | **Question: | ||
| If $P$ is invertible and $B = P^{-1}AP \Rightarrow \sigma(A) = \sigma(B)$. Why? | If $P$ is invertible and $B = P^{-1}AP \Rightarrow \sigma(A) = \sigma(B)$. Why? | ||
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| + | ==== Symmetric Matrices ==== | ||
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| + | Real matrix with real Eigenvalues is related to symmetric matrix. | ||
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| + | $S^T = S$ | ||
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| + | Positive semidefinite: | ||
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| + | Positive definite: $x^TSx > 0$ | ||
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| ==== Vector Spaces, Keywords ==== | ==== Vector Spaces, Keywords ==== | ||
mvg/lecture_02/start.1542630825.txt.gz · Last modified: 2018/11/19 12:33 by admin