Course Summary
This course covers matrix methods for solving linear equations, as well as eigenvalues and eigenvectors for understanding linear transformations.Key Learning Points
- Learn how to solve linear equations using matrix methods.
- Understand eigenvalues and eigenvectors and their applications in linear transformations.
- Apply matrix methods to solve real-world problems in physics, engineering, and computer science.
Related Topics for further study
Learning Outcomes
- Ability to solve linear equations using matrix methods
- Understanding of eigenvalues and eigenvectors and their applications
- Ability to apply matrix methods to solve real-world problems
Prerequisites or good to have knowledge before taking this course
- Basic understanding of algebra
- Familiarity with calculus
Course Difficulty Level
IntermediateCourse Format
- Online
- Self-paced
Similar Courses
- Linear Algebra - Foundations to Frontiers
- Matrix Algebra for Engineers
- Introduction to Linear Algebra
Related Education Paths
Notable People in This Field
- Grant Sanderson
- 3Blue1Brown
Related Books
Description
Mathematical Matrix Methods lie at the root of most methods of machine learning and data analysis of tabular data. Learn the basics of Matrix Methods, including matrix-matrix multiplication, solving linear equations, orthogonality, and best least squares approximation. Discover the Singular Value Decomposition that plays a fundamental role in dimensionality reduction, Principal Component Analysis, and noise reduction. Optional examples using Python are used to illustrate the concepts and allow the learner to experiment with the algorithms.
Outline
- Matrices as Mathematical Objects
- Matrix: Tabular Data
- Matrix Multiplication
- Supplement: Matrices in Python/Numpy
- Vector and Matrix operations
- Matrix Multiplication
- Matrix
- Matrix Multiplication and other Operations
- Matrix as Mathematical Objects
- Matrix Transpose
- Supplement: Matrix Transpose in Python
- Matrix Arithmetic
- Matrix Transpose
- Matrix Operations
- Matrix Transpose
- Systems of Linear Equations
- Systems of Linear Equations
- Solution of Linear Equations via Elimination
- LU Decomposition: Matrix is a Product of Simple Matrices
- Supplement: Solve Linear Equations in Python
- Systems of Linear Equations
- Gaussian Elimination Algorithm
- LU Decomposition
- Linear Least Squares
- Orthogonality and Inner Product.
- Linear Least Squares: Best Approximation
- Least Distance -> Orthogonality -> Normal Equations
- Example: Approximate Curve Fitting
- Orthogonality and the Inner Product
- Linear Least Squares
- Normal equations
- Approximate Curve Fitting
- Singular Value Decomposition
- S V D
- Latent Semantic Indexing
- SVD as a Decomposition
- SVD as a Data Analytics Tool
Summary of User Reviews
Learn the fundamentals of matrix methods in data analysis, signal processing, and machine learning through Coursera's Matrix Methods course. Highly rated by users, this course covers key aspects of matrix methods and offers both pros and cons for learners to consider.Key Aspect Users Liked About This Course
Many users praised the course's comprehensive coverage of matrix methods in data analysis, signal processing, and machine learning.Pros from User Reviews
- Great course for those with a strong math background
- In-depth coverage of matrix methods
- Excellent course material and assignments
- Good pace and clear explanations
Cons from User Reviews
- Can be difficult to follow if you don't have a strong math background
- Some of the assignments are quite challenging
- Not enough discussion or interaction with other students
- Could benefit from more real-world examples
Daniel Boley
4.1 Raiting
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