Linear Transformations of Euclidean Topological Spaces. Part II

For simplicity, we follow the rules: X denotes a set, n, m, k denote natural numbers, K denotes a field, f denotes an n-element real-valued finite sequence, and M denotes a matrix over RF of dimension n × m. One can prove the following propositions: (1) X is a linear combination of the n-dimension vector space over RF if and only if X is a linear combination of En T. (2) Let L2 be a linear combination of the n-dimension vector space over RF and L1 be a linear combination of En T. If L1 = L2, then the support of L1 = the support of L2. (3) Let F be a finite sequence of elements of En T, f1 be a function from En T into R, F1 be a finite sequence of elements of the n-dimension vector space over RF, and f2 be a function from the n-dimension vector space over RF into RF. If f1 = f2 and F = F1, then f1 F = f2 F1.