Chapter 2 Sums and quotients

  • Convention. In this chapter, all vector spaces are over the same field F unless we say otherwise.

2.1 Sums of subspaces

  • Definition. Let V1,,VkV. The sum V1++Vk is the set

    V1++Vk:={v1++vk|viVi,1ik}.

  • Proposition 2.1. Let V1,,VkV. Then

    • (1) V1++VkV.

    • (2) If WV and V1,,VkW then V1,,VkV1++VkW.