SM 1. Expand and compute the following double sums mr rs 2. Consider a group of...
ANSWER SHOULD BE NEAT CLEAN AND WELL EXPLAINED.HANDWRITTEN NEAT CLEAN,EACH STEP SHOULD BE EXPLAINED WELL Find the M to meet the Lyapunov equation in (3.59) with What are the eigenvalues of the Lyapunov equation? Is the Lyapunov equation singular? Is the solution unique? Repeat Problem 3.31 for B- Ci- A1 -2 with two different C 3.7 Lyapunov Equation Consider the equation AM +MB C (3.59) where A and B are, respectively, n x n andmx m constant matrices. In order...
2. Let F be a field, n > 1 an integer and consider the F-vector space Mat,,n(F) of n × n matrices over F. Given a matrix A = (aij) E Matn,n(F) and i < n let 1 row,(Α-Σ@y and col,(A)-Žaji CO j-1 j-1 be the sum of entries in row i and column i, respectively. Define C, A EMat,,(F): row,(A)col,(A) for all 1 < i,j < n] C, { A E Matn.n(F) : row,(A) = 0 = col,(A) for...