Segre characteristic of a square matrix

2020 Mathematics Subject Classification: Primary: 15A21 [MSN][ZBL]

Let $A$ be a square matrix over a field $F$ and let $\alpha \in \bar F$, the algebraic closure of $F$, be an eigenvalue of $A$. Over $\bar F$ the matrix $A$ can be put in Jordan normal form. The Segre characteristic of $A$ at the eigenvalue $\alpha$ is the sequence of sizes of the Jordan blocks of $A$ with eigenvalue $\alpha$ in non-increasing order. The Segre characteristic of $A$ consists of the complete set of data describing the Jordan normal form comprising all eigenvalues $\alpha_1,\ldots,\alpha_r$ and the Segre characteristic of $A$ at each of the $\alpha_i$.

See also: Segre classification.

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)