1. I.12 Linear Spaces
Condition: Does the linear space form a given set in which the sum of any two elements \ (x \) and \ (y \) and the work of any element \ (x \) are determined for any actual number \ (\ alpha \)? Set of all the vectors of space \ (\ mathbb {v} _ {3} \) lying on one axis; Sum: \ (x+y \), work \ (\ alpha | x | \).
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.