Detailed
Syllabus * 

Date 
Material 
Assignment 
Misc. 
January
4 
Introduction and motivation.  
January
7  12 
Defn
of v. space and subspace. Examples. Sum and intersection, direct
sum. Span. Linear dependence. 
Assignment
1 Solutions 

January
14  18 
Basis
and dimension. Coordinates
and change of basis. Linear maps: definitions and first examples. 
Assignment
2 Solutions 

January
21  25 
Dim(V) = dim(Ker) + dim(Im). Applications. Quotient spaces. Direct sums. Nipotent operators and projections. (Quiz 1)  Assignment
3 Solutions 

January
28  February 1 
Linear
maps and matrices. Signs of permuations. The existence of determinant. 
Assignment
4 Solutions 
Quiz
1: Jan 31, 16:00  17:30, MAASS 217

Feburary
4  February 8 
Uniqueness
and multiplicativity of determinants. Geomteric
interpretation of determinants. Laplace's formulas and the adjoint
matrix. Systems of linear equations. 
Assignment
5 Solutions 

February
11  15 
Row and column space and rank. Two matrices in REF with same rowspace are equal. Rank_r(A) = Rank_c(A). Calculating the inverse matrix. (Quiz 2)  Assignment
6 Solutions 
There are some typos
in the matrix in REF in question (1). (Some zeros need not be zeros..)
You all know how it's supposed to look like! 
February
18  22 
The
dual vector space. Inner
product spaces. CauchySchwartz inequality. 
Quiz 2: Feb
21, 16:00  17:30, RPHYS 118 RESULTS SOLUTIONS 

February
25  29 
Study Break  Study Break  Study Break 
March
3  7 
GramSchmidt.
Orthogonal projection. Eigenvalues
and eigenvectors. 
Assignment
7 Solutions 

March
10  14 
The
characteristic polynomial. Diagonalization. The
characteristic polynomial. Arithmetic and geometric
multiplicities. 
Assignment
8 Solutions 

March
17  19 
The minimal polynomial. CayleyHamilton. (Quiz 3) The primary decomposition theorem. Diagonalization again. Examples.  Assignment
9 Solutions 
Quiz 3: March 20,
16:30  18:00, MAASS 217 RESULTS SOLUTIONS typo: Exer. 3 refers to exer. 2 (and not 1). 
March
26  28 
The
Jordan canonical form. 
Assignment
10 Solutions 

March
31  April 4 
Symmetric and self adjoint operators. Applications: the Principal Axis Theorem, Inner products and more.  
April
7 April 11 
Normal operators. Bilinear forms. 