By Silvestre François Lacroix
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11) where Ers is the elementary matrix of ord~r (m X n) (the order of X) defined in section 1. 2. r =E~. 13) = [xii] is of order (m X n) A ::: [aii] is or order (l X m) and B = (h i/ ] is of order (n X q) Y = (Yij] is of ordeF (I X q) . A and B are assumed independent of X. Our aim is to find the rule for obtaining the derivatives ay and where X rs Is a typical elellll:nt of X and YI/Is a typicul element of Y. 13) as a function of the elements of X. We can achieve this objective in a number of different ways.
6 PROBLEM 4 We consider a problem similar to the previous one but in a different context. An important concept in Control Theory is the transition matrix. 13) Sec. J If A is a constant matrix, it is easily shown lhal Elements of Algebra by Silvestre François Lacroix
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