mvg:lecture_02:start
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===== Annotations / Comments / Remarks ===== | ===== Annotations / Comments / Remarks ===== | ||
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+ | ==== Special Euklidian Group SE(3) ==== | ||
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==== Eigenvalue Problem ==== | ==== Eigenvalue Problem ==== | ||
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+ | Linear transformation scales vector $\mathbf{v}$, | ||
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+ | Set of Eigen values is spectrum: | ||
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+ | $\sigma(A) = \{ \lambda_1 \ldots \lambda_n \} $ | ||
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+ | $A\mathbf{v} = \lambda \mathbf{v}$ | ||
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+ | $(A-\lambda \one) A = 0$ | ||
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+ | $\left(A-\lambda \unity \right) A = 0$ | ||
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+ | **Question: | ||
+ | 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.1542628605.txt.gz · Last modified: 2018/11/19 11:56 by admin