I am going to learn about matrices by myself. Can anyone recommend me some good books on matrices with exercises.
I personally enjoyed Linear Algebra and its Applications by David C. Lay.
This is an Indian high school textbook(pdf version).It does indeed teach matrices from scratch.Good luck!
For a freely available book (at least where I'm at) that's much more complete than what @Sanchayan Dutta gave, but still well below the level of what others have given, see the School Mathematics Study Group volume
The Table of Contents on pp. 8-9 gives a good description of what is covered.
The book was written in the 1960s for U.S. honors level high school students, my guess being those in approximately the top 10% of all students.
Books by Horn and Johnson are great resources for matrices. However, the books are not linear algebra textbooks so the basics of linear algebra and matrices you have to learn elsewhere. The first one reviews the required basics in the first chapter (numbered 0 on purpose).
- Matrix Analysis has a lot of material on eigenvalues and eigenvectors, canonical forms, matrix and vector norms. It also includes chapters on positive definite and nonnegative matrices.
- Topics in Matrix Analysis is more specialized to "unsorted" topics such as SVD, matrix functions, Hadamard and Kronecker products, stable matrices etc.
They include a lot of exercises throughout the text with solutions and a collection of interesting problems at the end of each section. I highly recommend it if you want to talk about matrices in a bar :-)
good luck for your studies...