I would great fully appreciative if someone could help me,step by step, given th
ID: 2938602 • Letter: I
Question
I would great fully appreciative if someone could help me,step by step, given this matrix, find the Jordan canonicalform for something like that, and explain me in details with whatis going on: M = -3 1 0 0 0 0 0 0 -3 1 0 0 0 0 0 0 -3 5 1 0 0 0 0 0 0 5 0 0 0 0 0 0 0 5 1 0 0 0 0 0 0 5 For the Jordan canonical form of the new matrix, does thismean that the matrix is always going to be nilpotent? Thank so much for help. Is the idea similiar to finding eigenspaces, i.e., do we haveto find the determinant, and the characteristic polynominal? How do you use the minimal polynominal - or is that notinvolved?? I would great fully appreciative if someone could help me,step by step, given this matrix, find the Jordan canonicalform for something like that, and explain me in details with whatis going on: M = -3 1 0 0 0 0 0 0 -3 1 0 0 0 0 0 0 -3 5 1 0 0 0 0 0 0 5 0 0 0 0 0 0 0 5 1 0 0 0 0 0 0 5 For the Jordan canonical form of the new matrix, does thismean that the matrix is always going to be nilpotent? Thank so much for help. Is the idea similiar to finding eigenspaces, i.e., do we haveto find the determinant, and the characteristic polynominal? How do you use the minimal polynominal - or is that notinvolved??Explanation / Answer
This matrix is already in Jordan canonical form. You have 3Jordan blocks, a 3x3 with -3 on the diagonal, and 2 2x2 blocks eachwith 5 on the diagonal. The characteristic polynomial for this would be (x + 3)^3 * (x -5)^4. The minimal polynomial would be (x + 3)^3 * (x -5)^2.