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MATH 235
LINEAR ALGEBRA 2
WINTER 2010
Course Objectives:
•
To understand several important concepts in linear algebra, including linear mappings and isomor
phisms; inner products and inner product spaces; orthonormal bases; orthogonal and symmetric
matrices; orthogonal diagonalization; quadratic forms; vector spaces over
C
; the real canonical
form; unitary, Hermitian, and normal matrices; unitary diagonalization.
•
To improve your ability to prove mathematical results.
•
To expand your knowledge of MATLAB.
Course Schedule
Week
Dates
Text Sections
Topics
1
Jan 4  8
45
Review 136, RankNullity Theorem
2
Jan 11  15
46, 47
Matrix of a Linear Mapping, Isomorphisms
3
Jan 18  22
47, 74, 71
Isomorphisms con’t, Inner Product Spaces, Orthogonality
4
Jan 25  29
71, 72
Orthonormal Basis, Orthogonal Matrix, Orthogonal Complement
5
Feb 1  5
72, 73
General Projections, GramSchmidt Procedure, Overdetermined Systems
6
Feb 8  12
73, 81
Least Squares, Diagonalization of Symmetric Matrices
7
Feb 15  19
READING WEEK
8
Feb 22  26
81, *, 82
Principal Axis Theorem, Triangularization, Quadratic Forms
9
Mar 1  5
82, 83, *
Quadratic Forms Con’t, Graphs of Quadratic Forms, SV Decomposition
10
Mar 8  12
*, 91
SVD con’t, Vector Spaces over
C
11
Mar 15  19
92, 93
Eigenvalues, Real Canonical Form, Complex Inner Products
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This note was uploaded on 04/18/2010 for the course MATH 235 taught by Professor Celmin during the Spring '08 term at Waterloo.
 Spring '08
 CELMIN
 Math, Algebra, Matrices

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