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CS223: Computational Linear Algebra by Rama
Chapter 0 – Introduction (التجربة المجانية)
Sample Lesson
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Chapter 0 – Introduction (التجربة المجانية)
5 Topics
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
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Chapter 1 – Introduction to Linear Systems
22 Topics
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
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Chapter 2 – Matrix Algebra
12 Topics
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
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Major #1
1 Topic
Major 1 – 251 old exam
Chapter 3 – Determinants
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Chapter 3 – Determinants
10 Topics
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
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Chapter 4 – Vector Spaces
14 Topics
4.1: Subspaces
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
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Major #2
1 Topic
Major 2 – 251 old exam
Chapter 5 – Eigenvalues and Eigenvectors
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Chapter 5 – Eigenvalues and Eigenvectors
14 Topics
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
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Chapter 6 – Orthogonality
14 Topics
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
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0.2: Course Content
⏱ 02:10
CS223: Computational Linear Algebra by Rama
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