1. Definitions and properties of f (A)
1.1 Examples of matrix functions
There are many applications involving matrix functions. We often manipulate matrix functions without realizing it. For example, when it exists, the inverse A -1 of A corresponds to the function such that f (x) = 1/x. Solving the linear system Ax = b means implicitly applying f (A) = A -1 to the vector b.
Another simple example is the solution of systems of linear differential equations involving the exponential function. We want to calculate y, solution of the equation
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Definitions and properties of f (A)
Methods for calculating f (A)
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