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Segre characteristic of a square matrix

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Let be a square matrix over a field and let , the algebraic closure of , be an eigenvalue (cf. Eigen value) of . Over the matrix can be put in Jordan normal form (see Jordan matrix). The Segre characteristic of at the eigenvalue is the sequence of sizes of the Jordan blocks of with eigenvalue in non-increasing order. The Segre characteristic of consists of the complete set of data describing the Jordan normal form comprising all eigenvalues and the Segre characteristic of at each of the .

References

[a1] H.W. Turnbull, A.C. Aitken, "An introduction to the theory of canonical matrices" , Blackie (1932) pp. Chapt. VI
[a2] Ch.G. Cullen, "Matrices and linear transformations" , Addison-Wesley (1972) pp. Chap. 5 (Dover reprint, 1990)
How to Cite This Entry:
Segre characteristic of a square matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Segre_characteristic_of_a_square_matrix&oldid=13050
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article