Introduction to Matrix Algebra is available as a MOOC now on Udemy. Of course, it is free! https://www.udemy.com/matrixalgebra/. You will have a lifetime access to 177 lectures, 14+ hours of high quality content, 10 textbook chapters complete with multiple choice questions and their complete solutions.
Learning Objectives are
- know vectors and their linear combinations and dot products
- know why we need matrix algebra and differentiate between various special matrices
- carry unary operations on matrices
- carry binary operations on matrices
- differentiate between inconsistent and consistent system of linear equations via finding rank of matrices
- differentiate between system of equations that have unique and infinite solutions
- use Gaussian elimination methods to find solution to a system of equations
- use LU decomposition to find solution to system of equations and know when to choose the method over Gaussain elimination
- use Gauss-Seidel method to solve a system of equations iteratively
- find quantitatively how adequate your solution is through the concept of condition numbers
- find eigenvectors and eigenvalues of a square matrix
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In a true Netflix style, on Halloween night, Friday October 31, 2014 at 11:59PM EST, we are releasing all resources simultaneously for an open courseware on Introduction to Matrix Algebra athttp://mathforcollege.com/ma/. The courseware will include
- 150 YouTube video lectures of total length of approximately 14 hours,
- 10 textbook chapters,
- 10 online multiple-choice quizzes with complete solutions,
- 10 problem sets, and
- PowerPoint presentations.
So set your calendar for October 31 for some matrix algebra binging rather than candy binging. For more info and questions, contact Autar Kaw.
Chapter 1: Introduction
Chapter 2: Vectors
Chapter 3: Binary Matrix Operations
Chapter 4: Unary Matrix Operations
Chapter 5: System of Equations
Chapter 6: Gaussian Elimination Method
Chapter 7: LU Decomposition
Chapter 8: Gauss-Seidel Method
Chapter 9: Adequacy of Solutions
Chapter 10: Eigenvalues and Eigenvectors
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A reader wrote: “I purchased on lulu the 2nd edition of your Introduction to Matrix Algebra for self study, and the book just arrived. I started reading it and found some annoying errors. For example on Chapter 1, page 5: for the first (diagonal) matrix, why is there a zero located in a33, when you defined on the previous page that only diagonal entries of square matrix can be non-zero (this answer is different on your free online pdf) . Also, on page 6 for the tridiagonal matrix, why is there a zero located in the diagonal below the major diagonal? I was wondering if you can provide me with the list of errors and corrections, because it’s going to be very difficult to study the material on my own and the errors in the book just makes it more frustrating.”
My answer: “There is no erratum issued yet on the book.
A diagonal matrix is diagonal based on the nondiagonal elements being zero. The diagonal elements have no restrictions. They can be zero or nonzero.
A tridiagonal matrix is a square matrix in which all elements not on the following are zero – the major diagonal, the above the major diagonal, and the diagonal below the major diagonal. The major diagonal, the diagonal above the major diagonal, and the diagonal below the major diagonal have no restrictions. They can be zero or nonzero.
The concerns you have raised are some of the common misconceptions students develop about these special matrices.
This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://nm.MathForCollege.com, the textbook on Numerical Methods with Applications available from the lulu storefront, the textbook on Introduction to Programming Concepts Using MATLAB, and the YouTube video lectures available at http://nm.MathForCollege.com/videos. Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.