Linear Algebra

~ Lecture Note 2009 Fall Semester ~

 

Professor Phong Q. Vu

Week 1

1.1 Vectors and Matrices in Engineering and Mathematics; n-Space

1.2 Dot Product and Orthogonality

 

Week 9

7.1 Basic and Demensions

7.2 Properties of Bases

     

Week 2

1.3 Vector Equations of Lines and Planes

2.1 Introduction to Systems of Linear Equations

2.2 Solving Linear Systems by Row Reduction

 

Week 10

7.3 The fundermental Space of Matrix

7.4 The Demension Theorem and Its Implications

7.5 The Rank Theorem and Its Implications

     

Week 3

3.1 Operations on Matrices

3.2 Inverse; Algebraic Properties of Matrices

3.3 Elementary Matrices; A Method for Finding A-1
 

Week 11

7.7 The Projection Theorem and Its Implication

7.9 Orthonormal Bases and the Gram-Schmidt process

     

Week 4

3.4 Subspaces and Linear Independence

3.5 The Geometry of Linear Systems

3.6 Matices with Special Forms

 

Week 12

8.1 Matrix Representations of Linear Trasformations

8.2 Similarity and Diagonalizability

8.3 Orthogonal Diagonalizability; Functions of a Matrix

     

Week 5

4.1 Determinants; Cofactor Expansion

4.2 Properties of Determinants

4.3 Cramer's Rule; Formula for A-1 ; Applications of Determinants
 

Week 13

8.4 Quadratic Forms

8.7 The Pseudoinverse

8.8 Complex Eigenvalues and Eigenvectors

     

Week 6

6.1 Matrices as Transformations

6.2 Geometry of Linear Operations

 

Week 14

8.9 Hermitian, Unitary, and Normal Matrices

     

Week 7

6.3 Kernel and Range

6.4 Composition and Invertibility of Linear Transformations

 

Week 15

9.1 Vector Space Axioms

9.2 Inner Product Spaces; Fourier Series

     

Week 8

  + Mid-Term
 

Week 16

  + Final Exam