Linear Algebra and Differential Equations
Basis functions are a set of linearly independent functions that span a function space, meaning any function within that space can be expressed as a linear combination of these basis functions. They serve as the building blocks for approximating more complex functions, especially in the context of least squares approximations, where finding the best fit to data is crucial. This concept is key when simplifying and solving problems by allowing for the representation of functions in a more manageable form.
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