The matrix exponential and initial value problems

Description
"The matrix exponential and initial value problems are discussed in this video lecture. The solution to the system of equation u' = Au is analysed. The solution of this system must denote a matrix, or
rather a matrix valued function. The fundamental matrix for the system is defined whose columns are independent solutions.Uncoupled and Defective examples are given on this context.Sometimes the matrix exponential can be a bit unexpected. There is no diagonal matrix, so it is defective, and we could find solutions by the standard method. However, it is also a companion matrix, for the second order equation.
Prof. Arthur Mattuck, Maths, 18.03.Differential Equations, Spring 2010: 27 28: Matrix Exponentials: Massachusetts Institute of Technology: MIT Open Course Ware),http://ocw.mit.edu (Accessed November 30, 2011). License: Creative Commons BY-NC-SA: http://ocw.mit.edu/terms/#cc