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One of the reasons for the importance of the matrix exponential is that it can be used to solve systems of linear ordinary differential equations.The solution of = (), =, where A is a constant matrix and y is a column vector, is given by =.
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
The exact origins of the LTE lemma are unclear; the result, with its present name and form, has only come into focus within the last 10 to 20 years. [1] However, several key ideas used in its proof were known to Gauss and referenced in his Disquisitiones Arithmeticae. [2]