Very clear and efficient in presenting proofs in class.

Professor Merkurjev is not a good teacher when it comes to undergraduate level classes. He's one of the best minds in algebra, so I don't think it occurred to him that an introductory linear algebra class could be hard to anyone, even if it is honors. Because of that, he would come into class, quickly go through the theorems on the board as if they were simple and obvious facts, and then leave. At the beginning, I tried following what he was saying as he lectured, but the material takes time to understand and he was sprinting through it, so I had to just copy down what he said and try to understand it later.

In all, the class was hard but I learned a lot from it. That came from putting a lot of time in at home, though, not from the professor. If I could take the class again, I would try to learn the material before going to class so I could get something out of his lectures. But if I could just teach myself the material like that, why would I need to take the class?

He's ok, to my point of view. I had a trouble with his Russian accent, but that shouldn't be a discouraging factor for anyone who's a true Math student. His lecturing speed is average for me, but he will be giving out a lot of great infos about algebra world. I learnt a lot about linear algebra through the course. Of course, the TA, Anthony Ruozzi, helped tremendously. Both are great algebraists, and I enjoyed being instructed by them.
His tests aren't hard. I thought I screwed up in the second midterm but as it turned out, I got the second highest score. 'Cuz he will give you partial credits. If you let him know where you are going with the proof, and if you're going in the right direction, he'll be very merciful if you make numerical mistakes.
His tests do require a lot of insights into algebraic structures though, but they are doable.
Overall, take him for algebra, you'll love it.

He was really a great professor, I would recommend him for any math course you can. While his exams are difficult he likes to give A's and grades were based on averages, not absolutes. You will come out of the class with a deeper understanding and love for Mathematics than when you entered.