1. FINITE-DIMENSIONAL VECTOR SPACES
... each xi ∈ F and n is any non-negative integer. Addition and scalar multiplication are defined in the obvious way. F[x] is clearly a vector space over F. Note that we could write the polynomial as an infinite sequence (a0, a1, …), but F[x] differs from F∞ in that here all the components from some poi ...
... each xi ∈ F and n is any non-negative integer. Addition and scalar multiplication are defined in the obvious way. F[x] is clearly a vector space over F. Note that we could write the polynomial as an infinite sequence (a0, a1, …), but F[x] differs from F∞ in that here all the components from some poi ...
Document
... 1. for the usual two and three dimensional vectors it is useful to express an arbitrary vector as a sum of unit vectors. 2. Similarly, the use of Fourier series for the analysis of functions is a very powerful tool in analysis. These two ideas are essentially the same thing when you look at them as ...
... 1. for the usual two and three dimensional vectors it is useful to express an arbitrary vector as a sum of unit vectors. 2. Similarly, the use of Fourier series for the analysis of functions is a very powerful tool in analysis. These two ideas are essentially the same thing when you look at them as ...
