On the elementary symmetric functions of a sum of matrices. (English) Zbl 1275.15005

Costas-Santos, R. S.

J. Algebra Number Theory, Adv. Appl. 1, No. 2, 99-112 (2009).

From the text: In Section 2 we present some results related with the determinant of sum of matrices, whose proof is given in the appendix. In Section 3 obtain the values of \(S_2(A + B)\) and \(S_3(A + B)\) by using the definition of the elementary symmetric functions of a matrix, in Section 4 we prove the same identities and also we obtain \(S_4(A + B)\) by using the Newton-Girard identities, where \(A\) and \(B\) are two generic \(n\)-by-\(n\) matrices.

MSC:

15A15	Determinants, permanents, traces, other special matrix functions
15A16	Matrix exponential and similar functions of matrices
05E05	Symmetric functions and generalizations