Isomorphic.md (895B)
1 # Isomorphic 2 3 **Source:** Linear Algebra Done Right 4 5 **Chapter:** 3 6 7 --- 8 9 Linear Algebra: 10 11 **Definition:** Two vector spaces are isomorphic if there is an invertible linear map from one vector space to to other. 12 13 Much the same as below; this invertible linear map can be thought of as a remapping of all elements from one space to another. 14 15 An important note about this is that: 16 17 two vector spaces are of the same dimension <-> they are isomorphic. 18 19 --- 20 21 Discrete Math (Graph Theory) 22 23 **Definition:** Two graphs are isomorphic if there is a function from V -> V_1 where V is the set of vertices of one graph and V_1 is the set of vertices in the other graph such that the edges of the graph are the same under the function. 24 25 This is to say; if there is a mapping of vertices between the two graphs that ensures all edges relationships are maintained in both graphs, then the two are isomorphic.