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CS223: Computational Linear Algebra by Rama

Chapter 0 – Introduction (التجربة المجانية) Sample Lesson

0.1: Course Introduction

0.2: Course Content

0.3: How to get an A+ in CS223

0.4: LU Factorization: Finding LU

0.5: Parametric Representation

Chapter 1 – Introduction to Linear Systems

1.1: Introduction to Linear Equations

1.2: Systems of Linear Equations

1.3: Introduction to Elementary Row Operations

1.4: Elementary Row Operations – Practice

1.5: Echelon Form and Reduced Echelon Form

1.6: Echelon Form PRACTICE

1.7: RREF PRACTICE

1.8: Parametric Representation

1.9: Vector Equations

1.10: Linear Combinations

1.11: The Matrix Equation Ax=b

1.12: Matrix-Vector Product (Row-Vector Rule)

1.13: Homogeneous Linear Systems (1)

1.14: Non-homogeneous Linear Systems (1)

1.15: Linear Independence (1)

1.16: Fast Way to Determine Linear Independence (1)

1.17: Introduction to Linear Transformation

1.18: The Matrix of a Linear Transformation

1.19: Existence and Uniqueness Questions

1.20: Worksheet Chapter 1: Questions 1 – 10

1.21: Worksheet Chapter 1: Questions 11-14

1.22: Worksheet Chapter 1: Questions 15 – 20

Chapter 2 – Matrix Algebra

2.1: Matrix Operations

2.2: Inverse of a 2 x 2 Matrix (1)

2.3: Elementary Matrices (1)

2.4: Algorithm to find A Inverse & the IMT (1)

2.5: LU Factorization Finding X using LU (1)

2.6: LU Factorization Finding LU (1)

2.7: Subspaces of Rn (1)

2.8: Column Space and Null Space of a Matrix

2.9: Dimension and Rank

2.10: Worksheet Chapter 2: Questions 1 – 5

2.11: Worksheet Chapter 2: Questions 6 – 8

2.12: Worksheet Chapter 2: Questions 9 – 12

Major 1 – 251 old exam

Chapter 3 – Determinants

3.1: Cofactor Expansion

3.2: Determinant of a Triangular Matrix

3.3: Determinant of Invertible and Noninvertible Matrices

3.4: 004. 3 x 3 Determinant Shortcut (optional)

3.5: Cramer’s Rule

3.6: A formula for A Inverse (Adjugate)

3.7: Determinants as Area or Volume

[NEW] Worksheet Chapter 3 Questions 1-3

3.9: Worksheet Chapter 3 Questions 4-7

3.10: Worksheet Chapter 3 Questions 8-10

Chapter 4 – Vector Spaces

4.2: The Null Space of a Matrix

4.3: The Column Space of a Matrix

4.4: The Contrast Between NulA and ColA

4.5: The Kernel and Range

4.6: Linearly Independent Sets; Bases

4.7: Bases for Nul A, Col A, and Row A

4.8: Coordinate Systems

4.9: The Dimension of a Vector Space

4.10: The Dimensions of Nul A, Col A, and Row A

4.11: Change of Basis

4.12: Worksheet Chapter 4: Questions 1 – 5

4.13: Worksheet Chapter 4: Questions 6 – 9

4.14: Worksheet Chapter 4: Questions 10 – 12

Major 2 – 251 old exam

Chapter 5 – Eigenvalues and Eigenvectors

5.1: Eigenvalues and Eigenvectors

5.2:Eigenvalues and Eigenvectors Continued..

5.3:The Characteristic Equation

5.4: Diagnolization

5.5: Diagnolization Full Example

5.6: Diagnolization Continued

5.7: Eigenvectors and Linear Transformations

5.8: Complex Eigenvalues

5.9: Real and Imaginary Parts of Vectors

5.10: The Power Method

5.10: Worksheet Chapter 5 : Questions 1-2

5.12: Worksheet Chapter 5 : Questions 3-6

5.13: Worksheet Chapter 5 : Questions 7-9

5.14: Worksheet Chapter 5 : Questions 10-11

Chapter 6 – Orthogonality

6.1: Inner Product, Length and Distance

6.2: Orthogonal Vectors and Orthogonal Complements

6.3: Orthogonal Sets

6.4: An Orthogonal Projection

6.5: Orthonormal Sets

6.6: Orthogonal Projections and Best Approximation Theorm

6.7: The Gram-Schmidt Process

6.8: Orthonormal Bases

6.9: QR Factorization

6.10: Least-Squares Problems

6.11: Alternative Calculations of Least-Squares Solution

6.12: Worksheet Chapter 6: Questions 1 – 2

6.13: Worksheet Chapter 6: Questions 3

6.14: Worksheet Chapter 6: Questions 4 – 6

0.5: Parametric Representation

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CS223: Computational Linear Algebra by Rama 399.00

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