126
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(K) = f (K). Thus we get
det(A) =
f (K) =
g(h(K) =
g(K)
22
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 chapter, these questions can be answered on the case-by-ca
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,
which we call the integers. We are also familiar with (a
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 ideas from one setting to a new
setting that shares so
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 (S) is the tuple
(f (u1 ), ., f (un ) V n . If S = (u1
Math 22a, Introduction to Linear Algebra
Fall 2015
Venue: Goldsmith Rm 116
Time: TTh 2:00-3:20, F 2:00-2:50, Block N+S5.
Instructor: Bong Lian (lian@, Goldsmith 314, X6-3069)
Oce Hours: TTh 12:30-1:30, or by appointment
I will use the LATTE forum to commu