Vector space isomorphism ↩

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created: 2021-11-06 13:06:30
modified: 2022-01-10 04:13:04

1. is surjective if (with other notation: ).
2. is injective if its kernel only contains the zero vector:

A linear map which is both surjective and injective (bijective in other words) is an isomorphism.

If there is an isomorphism from to , we say that they are isomorphic and write .

Comments

• Inverse of vector space isomorphism is also linear
• An isomorphism maps a zero vector to a zero vector
• Isomorphism is an equivalence relation between vector spaces
• Vector spaces of same dimension are isomorphic
• Isomorphic vector spaces have the same dimension
• Each finite-dimensional vector space is isomorphic to one and only one of the