Linear Algebra Basics by Coursera
Course Highlights
- Describe the vector spaces, vector subspaces, basis, and dimension of a vector space.
- Explain the linear transformations defined on vector spaces and eigenvalues and eigenvector of a matrix, symmetric and skew-symmetric matrices.
- Explain diagonalizable matrices, their applications and the inner product, and the norm of vectors and matrices.
Skills you will learn!
Curriculum
2 Topics
Course Overview
Meet and Greet
10 Topics
Binary Operations
Vector Space - I
Vector Space - II
Vector Subspace
Linearly Dependence and Independence of Vectors
Linear Combination and Linear Span of Vectors
Essential Reading: Real Vector Space
Recommended Reading: Real Vector Space
Practice Quiz: Week 1
Graded Quiz: Week 1
13 Topics
Basis and Dimension of a Vector Space
Linear Transformations
Null Space of a Linear Transformation
Range Space of a Linear Transformation
Matrix Associated with a Linear Transformation
Eigenvalues of a Matrix
Essential Reading: Basis and Dimension of a Vector Space
Essential Reading: Linear Transformations
Recommended Reading: Linear Transformations
Essential Reading: Eigenvalues of a Matrix
Live Session 1
Practice Quiz: Week 2
Graded Quiz: Week 2
11 Topics
Eigenvector of a Matrix
Special Matrices and Their Properties
Similar Matrices
Diagonalizable Matrices - I
Diagonalizable Matrices - II
Applications of Diagonalization of a Matrix
Essential Reading: Diagonalizable Matrices
Recommended Reading: Diagonalizable Matrices
Live Session 2
Practice Quiz: Week 3
Graded Quiz: Week 3
12 Topics
Spectral Decomposition
Singular Value Decomposition - I
Singular Value Decomposition - II
Applications of Singular Value Decomposition
Inner Product Space
Vector and Matrix Norms
Essential Reading: Spectral Decomposition and Singular Value Decomposition
Recommended Reading: Spectral Decomposition and Singular Value Decomposition
Essential Reading: Inner Product and Vector Norms
Live Session 3
Practice Quiz: Week 4
Graded Quiz: Week 4
5 Topics
How to Attempt and Submit the Assignment
Introduction to Python for Linear Algebra
How to Use Coursera Jupyter Lab
Linear Algebra Basics Using Python
Jupyter Lab for Assignment
Linear Algebra Basics
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