On the Segre characteristic of a block triangular matrix Original Research Article

Consider two complex matrices A and B of sizes n×n and m×m respectively, and let λ be an eigenvalue of both matrices. If α=(n1,n2) and β=(m1,m2) are the Segre characteristics associated with λ of A and B, respectively, and γ=(r1,r2,r3,r4) is a nonincreasing sequence of nonnegative integers, then a method for determining when γ is the Segre characteristic of the block triangular matrix image in terms of α and β, and the structure of matrix L is presented. A completely explicit description of the Segre characteristic of M associated with λ is obtained. Using similar techniques, general cases when α, β and γ have more elements and satisfy some size restrictions are considered.