Linear Algebra Done Right · Problem 1C.17

Finite-Dimensional Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · sums-of-subspaces

Problem

Is the operation of addition on the subspaces of VV associative? In other words, if V1,V2,V3V_1, V_2, V_3 are subspaces of VV, is (V1+V2)+V3=V1+(V2+V3)?(V_1 + V_2) + V_3 = V_1 + (V_2 + V_3)?

Related theory

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