Closed-form expressions of the eigen decomposition of 2 x 2 and 3 x 3 Hermitian matrices

Abstract : The eigen decomposition of covariance matrices is at the core of many data analysis techniques. The study of 2-components or 3-components vector fields typically requires computing numerous eigen decompositions of 2 x 2 or 3 x 3 matrices. This is, for example, the case in the analysis of interferometric or polarimetric SAR images, see MuLoG algorithm (https://hal.archives-ouvertes.fr/hal-01388858). The closed-form expression of eigen-values and eigenvectors then provides a way to derive faster data processing algorithms. This note gives these expressions in the general case (special cases where some coefficients are zero, or the eigenvalues are not separated may not be covered and then require either to introduce a small perturbation of the initial matrix or to derive other expressions).
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Rapport
[Research Report] Université de Lyon. 2017
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https://hal.archives-ouvertes.fr/hal-01501221
Contributeur : Loïc Denis <>
Soumis le : mardi 4 avril 2017 - 08:38:09
Dernière modification le : dimanche 9 avril 2017 - 01:06:59

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matrix_exp_and_log_formula.pdf
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  • HAL Id : hal-01501221, version 1

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Charles-Alban Deledalle, Loic Denis, Sonia Tabti, Florence Tupin. Closed-form expressions of the eigen decomposition of 2 x 2 and 3 x 3 Hermitian matrices. [Research Report] Université de Lyon. 2017. <hal-01501221>

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