Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
vmls-book.stanford.edu
Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
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Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#2I'm going to complain about this every chance I get.
A 2D vector, we generally store as [x, y, 0]. What's the extra 0? The homogeneous coordinate.
A 2D point, we generally store as [x, y, 1]. That extra 1 is the homogeneous coordinate, and since it's there, it means "and apply translations!"
If I have a 2D transform, I put the translation component in the last row or column, depending on if you pre-multiply or post-multiply (I can never remember which).
When I transform a vector by that matrix, the 0 in the homogeneous coordinate means translation doesn't apply.
Perfect!
But what if I have a 3D vector? Well... I end up with [x, y, z, 0], right?
Ugh.
If instead, we stored the homogeneous coordinate in the FIRST position, [0, x, y] for 2D, and [0, x, y, z] for 3D, etc. then it's just a sparse vector! Set the values you want to! [0] is the 0-vector in any number of dimensions!
[1] is the origin point in any number of dimensions!
Why did we put the homogeneous coordinate last in all our internal representations? It was so dumb!
Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#3I'm going to complain about this every chance I get. A 2D vector, we generally store as [x, y, 0]. What's the extra 0? The homogeneous coordinate. A 2D point, we generally store as [x, y, 1]. That extra 1 is the homogeneous coordinate, and since it's there, it means "and apply translations!" If I have a 2D transform, I put the translation component in the last row or column, depending on if you pre-multiply or post-m…
I don't follow. What do we gain by moving the homogeneous coordinate from last position to first?
I don't understand this:
> then it's just a sparse vector! Set the variables you want to!
Or this:
> [1] is the origin point in any number of dimensions.
Could you clarify?
Also, I don't think this book even discusses homogeneous coordinates. It would be sort of unusual for this type of general text and the only mention of "homogeneous" in the index is "homogeneous equation."
Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#4I'm e-learning Linear Algebra right now to have a good math foundation for Machine Learning.
I was a History and Sociology major in college - so I didn't take any math.
If you are like me, and working off an initial base of high school math, I would recommend the following (all free):
Linear Algebra Foundations to Frontiers (UT Austin) Course: https://www.edx.org/course/linear-algebra-foundations-to-fro... Comments: This was a great starting place for me. Good interactive HW exercises, very clear instruction and time-efficient.
Linear Algebra (MIT OpenCourseware) Course: https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra... Comments: This course is apparently the holy grail course for Intro Linear Algebra. One of my colleagues, who did an MS in EE at MIT, said Gilbert Strang was the best teacher he had. I started off with this but had to rewind to the UT class because I didn't have some of the fundamentals (e.g. how to calc a dot product). I'm personally 15% through this, but enjoying it.
Linear Algebra Review PDF (Stanford CS229) Link: http://cs229.stanford.edu/section/cs229-linalg.pdf Comments: This is the set of Linear Algebra review materials they go over at the beginning of Stanford's machine learning class (CS229). This is my workback to know I'm tracking to the right set of knowledge, and thus far, the courses have done a great job of doing so.
Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#5After reading this book (or during), take a look at the author's (Boyd) video lectures on linear dynamical systems: https://see.stanford.edu/Course/EE263/
There is a lot of overlap between the book and the course.
Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#6This is a beautiful book and a great intro to the basics of linear algebra. All the figures in the book are generated in Julia and there’s a companion book with Julia code for computational examples:
Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#7I'm e-learning Linear Algebra right now to have a good math foundation for Machine Learning. I was a History and Sociology major in college - so I didn't take any math. If you are like me, and working off an initial base of high school math, I would recommend the following (all free): Linear Algebra Foundations to Frontiers (UT Austin) Course: https://www.edx.org/course/linear-algebra-foundations-to-fro... Comments:…
Don't forget to review calculus as well. Khan Academy is a good start for learning about single variable calculus (http://www.khanacademy.org), but their content on multivariable calculus is a bit lacking (neural networks / deep learning use the concept of the derivatives and the gradient a lot). A good supplement for multivariable calculus would be Terence Parr and Jeremy Howard's article on "All the matrix calculus you need for deep learning": https://explained.ai/matrix-calculus/index.html
Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#8Just finished my intro linear algebra class yesterday.
The class was a bit more abstract in nature, so some of the chapters in this look like they could be nice application oriented follow ups to it!
Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#9I'm e-learning Linear Algebra right now to have a good math foundation for Machine Learning. I was a History and Sociology major in college - so I didn't take any math. If you are like me, and working off an initial base of high school math, I would recommend the following (all free): Linear Algebra Foundations to Frontiers (UT Austin) Course: https://www.edx.org/course/linear-algebra-foundations-to-fro... Comments:…
Don't forget to review calculus as well. Khan Academy is a good start for learning about single variable calculus ( http://www.khanacademy.org ), but their content on multivariable calculus is a bit lacking (neural networks / deep learning use the concept of the derivatives and the gradient a lot). A good supplement for multivariable calculus would be Terence Parr and Jeremy Howard's article on "All the matrix calcul…
Thanks - I am doing that as well! I've been using MIT OpenCourseware for single variable calculus (and will do the same for multivariable). I fenced the parent post to Linear Algebra to not go too far away from the OP.
I will certainly check out the Terrence Parr / Jeremy Howard site, and am super familiar with Khan Academy.
Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#10How much overlap is there between this and Stanford's EE263?
Can someone in the know comment on the differences between what is covered?