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
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
3.6 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
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
Week 16
+ Final Exam