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Jow
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I want to beginning learning linear algebra. I will be studying it on my own, so I was wondering what the best book would be.
micromass said:Depends on you. There is no objective best book, there are only book which you like or dislike.
Anyway, what kind of math do you know already?? Are you familiar with matrices and determinants?? Are you familiar with proofs?? "Analytic" geometry?? Abstract algebra?? Are you wanting to be a physicist or a mathematician?? etc.
Klungo said:One good question would be:
Do you want a computational emphasis on linear algebra?
Or a more theoretical approach? (Which requires proficiency in proof writing and logical reasoning)
Usually, the proof based course covers the computational side in sufficient detail. Think of the theoretical side as making all the formulas and algorithms in the computational linear algebra course legitimate.
Jow said:Well I am sure I would enjoy a theoretical approach more, but I think a more computational emphasis would be better for me. The reason I am self studying all of these topics is so that when I get into university I will already have a decent understanding of the topics.
Vargo said:There are lots of books on the subject and it is hard to agree on a best book. I learned from Hoffman and Kunze, but that's a bit dry for some (see Amazon reviews). Since you want to go into physics, a good Russian standard would probably serve you well.
https://www.amazon.com/dp/048663518X/?tag=pfamazon01-20
Vargo said:Good point. I am definitely not sure whether it is suitable for someone still in high school who does not know about matrices. But its a Dover book, so it is cheap :) At least, it would be great alongside another book that is more elementary. In the worst case scenario, if it is too hard, you can put it on the shelf and take it down again when you are ready.
Jow said:Due to these comments I have looked into matrices. I know how to add, subtract and find their inverses, as well as how to solve system of equations and vector combination problems. Not to say that I know a lot about matrices, but I at least know some of the basics.
Linear algebra is a branch of mathematics that deals with the study of linear equations and their representations in vector spaces. It involves the use of matrices, vectors, and linear transformations to solve mathematical problems.
Linear algebra is essential in many areas of science, technology, and engineering. It is used to solve complex problems in fields such as physics, computer graphics, data analysis, and machine learning. It also provides a foundation for advanced mathematics courses.
There are many excellent books on linear algebra, but some popular choices include "Linear Algebra and Its Applications" by David C. Lay, "Introduction to Linear Algebra" by Gilbert Strang, and "Linear Algebra Done Right" by Sheldon Axler. It ultimately depends on your learning style and level of mathematical background.
A good linear algebra book should have clear explanations, plenty of examples and practice problems, and a good balance between theory and applications. It should also cover key topics such as vector spaces, matrices, determinants, eigenvalues and eigenvectors, and linear transformations.
Some knowledge of basic algebra, including solving equations, working with variables, and understanding functions, is necessary for learning linear algebra. It is also helpful to have a basic understanding of geometry and trigonometry. However, with dedication and a good textbook, anyone can learn linear algebra.