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3 cards from this section. Quick, good the night before a test.
Define vector space isomorphism.
Look for the main definition and how it involves transformations.
What is a bijective function?
Remember the terms one-to-one and onto.
What does it mean for two vector spaces to be isomorphic?
Think about how structures relate to each other.
Is it true or false that any two vector spaces of different dimensions can be isomorphic?
Recall the essential property of isomorphic spaces.
Prove that if two spaces are isomorphic, then any linear transformation defined on one can be transferred to the other.
Refer back to the definitions of linear transformations and how they interact with vector operations.
Given a vector space V with basis vectors (1, 0) and (0, 1), determine if the space spanned by (2, 0) and (0, 3) is isomorphic to V.
Convert the new basis vectors to the original basis structure and check for linear transformations.
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