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Basis and Components Explained Visually | Why u = ui ei?
What are the basis and components of a vector? A vector is the actual geometric object. Its components are the numbers used to describe that vector in a chosen basis. If e1, e2, e3 form a basis, then any vector u can be written as u = u1 e1 + u2 e2 + u3 e3 Using Einstein summation notation, this becomes u = ui ei where repeated index i is ...
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