SumOfVectorSpaces.md (647B)
1 # Sum of Vector Spaces 2 3 **Source:** Linear Algebra Done Right 4 5 **Chapter:** 1 6 7 **Definition:** The sum of two vector spaces is another vector space which is formed by all sums of vectors in both spaces (think combining each vector with every other vector). 8 9 Note that the sum of vector spaces is not simply limited to two vector spaces and can be stated as follows for 3 vector spaces where V_1, V_2, V_3 are vector spaces as is S_1: 10 11 S_1 = V_1 + V_2 + V_3 12 13 ### Other Information 14 15 1. If U_1, U_2, U_3 are subspaces of V then so is U_1 + U_2 + U_3 16 2. The smallest possible subspace that contains U_1, U_2, and U_3 is the sum of their vector spaces