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Linear Algebra

Course Customised for: Linear Algebra

Course taught by: Amos Bahiri

55h

9 Downloadable Resources

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Course syllabus

1. Systems of Linear Equations
Workbook
4h 28m
Systems of Linear Equations preview
SLE with Parameter preview
SLE over Zp preview
2. Matrices
Workbook
5h 11m
Matrix Inverse and its Applications preview
Properties of the Matrix Inverse preview
Matrix and Basic Operations on Matrices preview
Elementary Matrices and LU Decomposition preview
3. Determinants
Workbook
5h 3m
Determinants preview
Rules of Determinants preview
More Rules of Determinants preview
Cramer's Rule preview
The Adjoint Matrix preview
Geometrical Applications of Determinants preview
4. Vector Spaces over R (Rn)
4h 58m
The Vector Space Rn preview
Linear Combination, Dependence and Span preview
Basis for Rn preview
Solution Space of Homogenous SLE preview
Subspaces preview
Row and Column Spaces preview
Change of Basis preview
5. Fields
1h 54m
Fields preview
6. General Vector Spaces
4h 22m
Vector Spaces preview
Linear Combination, Dependence and Span preview
Vector Basis preview
Solution Space of Homogenous SLE preview
Subspaces preview
Change of Basis preview
7. Linear Transformations
Workbook
4h 53m
Linear Transformation Definition preview
Image and Kernel preview
Isomorphism and Inverse preview
Composition of Linear Transformations preview
8. Matrix of Linear Transformations
Workbook
1h 32m
Reminder - Coordinate Vectors and Change of Basis preview
Matrix of Linear Transformation preview
9. Eigenvectors Eigenvalues and Diagonalization
Workbook
8h 28m
Eigenvectors and Eigenvalues of a Matrix preview
Matrix Similarity preview
Matrix Diagonalization preview
Cayley-Hamilton theorem and the Minimal Polynomial preview
Linear Transformation's Eigenvalues and Diagonalization preview
10. Inner Product Spaces
Workbook
6h 6m
Inner Product Spaces preview
Norm and Distance preview
Cauchy–Schwarz Inequality preview
Orthogonality preview
Orthogonal Complement preview
Orthogonal Sets and Bases preview
11. Vectors
Workbook
6h 44m
Introduction to 2D and 3D Vectors preview
Vector Arithmetic preview
Vectors Dot Product preview
Vectors Cross Product preview
The 3D Coordinates System preview
Equations of Lines preview
Equations of Planes preview
Quadric Surfaces preview
12. Markov Chains
Workbook
42m
Markov Chains preview
Mr. Amos Bahiri
About

Amos Bahiri earned his undergraduate degree in Mathematics, and then went on to earn two Master’s Degrees (MS) in Mathematics and Computer & Information Science from Ohio State University. In addition to being an outstanding instructor of mathematics, Amos is known for his math jokes.