
1. I.13 Linear Spaces
Condition: let \ (v \)-linear space of all polynomials over \ (\ mathbb {r} \) degree \ (\ leq 5 \), a \ (v \)-the bilinear form on \ (v \), set by the formula \ (\ quad v (p, p, p, p, p (p, p, p, p (p, p q) = \ sum_ {k = 1}^{n} p (k) q (k) \). At what values \ (n \) the form \ (v \) is shown by a scalar work on \ (v \)?
Linear Spaces, Subspaces. Investigation of Given Sets with Operations Defined on Them to Compose a Linear Space. Axioms of Linear Spaces. Linear Spaces of Polynomials, Matrices, Vectors, Functions and Numbers.