# Good set of exercises with solutions for linear algebra

I'm trying to get a solid knowledge of linear algebra for statistics and machine learning. I didn't study math during college/university. I have the very basic knowledge of what is a dot product, a matrix inverse, and a transpose, but I tend to stumble on concepts like rank of a matrix. There are several books out there to learn linear algebra (to name just a couple):

However, whichever course of stat / math you take starts always with the teacher saying: "Only listening to my class is useless if you don't do the exercises". Alright, but if you are studying on your own, you also need the answers (being confident that your answer to an exercise is the right one when you are actually flatly wrong is astonishingly easy according to my own experience...). The above mentioned books have exercises but don't provide the answers. Could somebody recommend a source of exercises with solutions with the final goal of being able to understand (at least a little better) a reference book of machine learning like The Elements of Statistical Learning by Hastie and Tibshirani?

Give Linear Algebra Problem Book by Paul Halmos a try. It is written in a conversational style and has both hints and solutions at the back of the book.

Another book that has answers to exercises is Jim Hefferon's Linear Algebra, which is freely available online, but I personally have not read it.

• thanks @ffffforall for your answer! I 'm going to check it out.
– ecjb
Feb 1, 2019 at 21:48

Out of my favorite texts on linear algebra, three have solved exercises:

The first one is a vector-space-based approach while the second is all about matrices. Both are mathematically rigorous and (for all I have checked) written well. I have no experience with the third. I don't know if they take you all the way to the beginning of a machine learning text -- it might need some linear optimization too?

Let me also mention two other resources:

• Many thanks for your answer, @darjgrinberg. Those two texts seem very straightforward and of very good quality. Indeed you're definitely right for linear optimization. Do you have a text with exercices and answers to recommend for this topic?
– ecjb
Feb 3, 2019 at 8:02
• None that I know of. Niels Lauritzen's Undergraduate Convexity (not a free resource, sadly) is a great textbook but I don't think it has any solved exercises. Feb 3, 2019 at 17:29

I really like Linear Algebra and It's Applications by Lay. I'm in an applied linear algebra class at the moment and I find the book very concise and helpful. It also has solutions in the back for odd numbered exercises.

• many thanks for your comment @Matthew, I will check it out!
– ecjb
Feb 3, 2019 at 7:59