- #1

schniefen

- 164

- 4

- TL;DR Summary
- Understanding the linear transformation of ##F(\mathbf{u})(t)=\mathbf{u}^{(n)}(t)+a_1\mathbf{u}^{(n-1)}(t)+...+a_n\mathbf{u}(t)##.

How can the function ##F(\mathbf{u})(t)=\mathbf{u}^{(n)}(t)+a_1\mathbf{u}^{(n-1)}(t)+...+a_n\mathbf{u}(t)##, where ##\mathbf{u}\in U=C^n(\mathbf{R})## (i.e. the space of all ##n## times continuously differentiable functions on ##\mathbf{R}##) be a linear transformation (from ##U##) to ##V=C(\mathbf{R})##? In ##F##, isn't the term ##\mathbf{u}^{(n)}(t)## not eliminable and so one always gets a vector in ##C^n(\mathbf{R})##?

Last edited: