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Now the correspondence K L is one-to-one (because K can be recovered from L by
reversing the swaps). This correspondence denes a one-to-one map h : K L on the set
of permutations.
By denition g(h(
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1.7. A preview
This chapter teaches us a mechanical way to solve any given linear system. How
many solutions are there? How do all the solutions hang together? With the tools introduced in this cha
LINEAR ALGEBRA LECTURE NOTES
BONG H. LIAN
1. Algebra of numbers, sets, and maps
Lets start with some basic aspects of numbers, sets, and maps. We are familiar with
the numbers,
, 2, 1, 0, 1, 2, 3,
w
LINEAR ALGEBRA LECTURE NOTES
25
9. Abstract vector spaces
When we study examples of elds and 1-variable equations, we have seen that abstraction can be very useful way to transfer one set of tools and
LINEAR ALGEBRA LECTURE NOTES
39
13. Conservation of Dimension
Throughout this section, U, V, W will denote nite dimensional vector spaces.
If f : U V is a linear map, and S = (u1 , ., un ) U n then f