# Elementary symmetric of a sum of matrices

 Importance: High ✭✭✭
 Author(s):
 Subject: Algebra
 Keywords:
 Posted by: rscosa on: December 8th, 2008
Problem

Given a Matrix , the -th elementary symmetric function of , namely , is defined as the sum of all -by- principal minors.

Find a closed expression for the -th elementary symmetric function of a sum of N -by- matrices, with by using partitions.

The Newton-Girard formulas imply particular expressions for small values of and , for example, .

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that's ok