Why is differentiation not a linear transformation from v

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Properties of Splines and Linear Transformations

Show that the set of natural cubic splines on a given know partition x_0 < x_1 < ... < x_a is a vector space, V say. Show that V is of dimension n + 1.

Why is differentiation not a linear transformation from V to V? What is the image of V under the operation of taking the second derivative?

Reference no: EM13123740

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