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.
What's included
3 videos2 readings3 assignments
Show info about module content
3 videos•Total 11 minutes
Matrix: Tabular Data•3 minutes
Matrix Multiplication•5 minutes
Supplement: Matrices in Python/Numpy•2 minutes
2 readings•Total 40 minutes
Vector and Matrix operations•30 minutes
Matrix Multiplication•10 minutes
3 assignments•Total 30 minutes
Matrix•30 minutes
Linear combinations•0 minutes
Matrix Combinations•0 minutes
Matrix Multiplication and other Operations
Module 2•2 hours to complete
Module details
What's included
3 videos2 readings3 assignments
Show info about module content
3 videos•Total 14 minutes
Matrix as Mathematical Objects•4 minutes
Matrix Transpose•5 minutes
Supplement: Matrix Transpose in Python•5 minutes
2 readings•Total 20 minutes
Matrix Arithmetic•10 minutes
Matrix Transpose•10 minutes
3 assignments•Total 60 minutes
Matrix Operations•30 minutes
Matrix Transpose•30 minutes
Matrix Multiplication and Other Operations•0 minutes
Systems of Linear Equations
Module 3•1 hour to complete
Module details
What's included
4 videos3 readings4 assignments
Show info about module content
4 videos•Total 15 minutes
Systems of Linear Equations•4 minutes
Solution of Linear Equations via Elimination•3 minutes
LU Decomposition: Matrix is a Product of Simple Matrices•6 minutes
Supplement: Solve Linear Equations in Python•3 minutes
3 readings•Total 30 minutes
Systems of Linear Equations•10 minutes
Gaussian Elimination Algorithm•10 minutes
LU Decomposition•10 minutes
4 assignments
Systems of Linear Equations•0 minutes
Solution of Linear Equations via Elimination•0 minutes
LU Decomposition•0 minutes
Systems of linear equations•0 minutes
Linear Least Squares
Module 4•2 hours to complete
Module details
What's included
4 videos2 readings5 assignments
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4 videos•Total 16 minutes
Orthogonality and Inner Product.•4 minutes
Linear Least Squares: Best Approximation•3 minutes
Least Distance -> Orthogonality -> Normal Equations•5 minutes
Example: Approximate Curve Fitting•5 minutes
2 readings•Total 20 minutes
Orthogonality and the Inner Product•10 minutes
Linear Least Squares•10 minutes
5 assignments•Total 60 minutes
Orthogonality and Inner Product•0 minutes
Linear Least Squares•0 minutes
Normal equations•30 minutes
Approximate Curve Fitting•30 minutes
Linear Least Squares•0 minutes
Singular Value Decomposition
Module 5•1 hour to complete
Module details
What's included
2 readings3 assignments
Show info about module content
2 readings•Total 20 minutes
S V D•10 minutes
Latent Semantic Indexing•10 minutes
3 assignments•Total 60 minutes
SVD as a Decomposition•30 minutes
SVD as a Data Analytics Tool•30 minutes
Singular Value Decomposition•0 minutes
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