How is the Jordan form related to the matrix exponential?
Submitted by: demetri Submitted on: October 8, 2003 Identifier: L2.2 First, one should check the previous FAQ(s) on Jordan form. Second, we promise that all relevant material on Jordan forms will be presented as needed in class 🙂 Having said that, the Jordan form of a matrix (say A) satisfies a “similarity” relation: A = TJT-1 Here T is the matrix of (generalized) eigenvectors of A. Let’s check out the square of A: A2 = TJT-1TJT-1 = TJ2T-1 Thus, we can move power series (and by extension, exponentiation) “inside” the similarity transformation defined by T. This is very useful because exponentiating Jordan blocks is much easier than exponentiating general matrices (see the associated FAQs for these issues). Hence, the Jordan form gives a convenient formula for exponentiation of a matrix. [Back to Top] • Why are the two main principles of control presented in L1.1 called “principles”? Why are there only two of them? Submitted by: lars Submitted on: October 9, 2003 Identifier: L1.1 [Con
