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