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numerical-range:generalizations:c-perturbation-of-unitary-matrix-numerical-range

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numerical-range:generalizations:c-perturbation-of-unitary-matrix-numerical-range [2019/07/24 12:36]
plewandowska
numerical-range:generalizations:c-perturbation-of-unitary-matrix-numerical-range [2019/07/24 12:38]
plewandowska
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 ===== Illustration of above theorem ===== ===== Illustration of above theorem =====
-For each eigenvalue we mark its instantaneous velocity given by formula $\sum\limits_{i=1}^d\ p_i |\braket{i}{x}|^2 $. Red colour denotes instantaneous velocity equal to one and blue colour corresponds to the instantaneous velocity equal to zero. +For each eigenvalue ​$\lambda(t)$ of matrix $UE(t)$ ​we mark its instantaneous velocity given by formula $\sum\limits_{i=1}^d\ p_i |\braket{i}{x(t)}|^2 $, where $\ket{x(t)}$ is corresponding eigenvector. Red colour denotes instantaneous velocity equal to one and blue colour corresponds to the instantaneous velocity equal to zero. 
 === Example 1 === === Example 1 ===
 Diagonal matrix ​ Diagonal matrix ​
numerical-range/generalizations/c-perturbation-of-unitary-matrix-numerical-range.txt · Last modified: 2020/02/19 08:01 by rkukulski