Week 1
1.1 Vectors and Matrices in Engineering and Mathematics; nSpace
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 GramSchmidt 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
+ MidTerm 

Week 16
+ Final Exam
