Unique identity and inverse question.

  • Thread starter loli12
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loli12

Main Question or Discussion Point

When we say that the identity and inverse element in a vector space is unique, does it mean that those elements are the same for all x in V? or does it mean that each x has its own unique identity or inverse element?

moreover, is there a geometric way of explaning what a field is? because I got confused about the scalar multiplication of a vector space that b in F and c in V which give bc in V..

and also, did anyone used Linear Algebra by Friedberg, Insel and Spense before? What do you think about the book?
 

Answers and Replies

  • #2
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unique identity means the whole algebraic system (group, ring or field, etc) has exactly one element e with the property that ae = ea = a for EVERY a in the object you're interested in. same goes for 'unique inverse' & so on.
 

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