Best advanced linear algebra book
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Advanced Linear Algebra
Linear algebra is the branch of mathematics concerning linear equations such as. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry , including for defining basic objects such as lines , planes and rotations. Also, functional analysis may be basically viewed as the application of linear algebra to spaces of functions. Linear algebra is also used in most sciences and engineering areas, because it allows modeling many natural phenomena, and efficiently computing with such models. For nonlinear systems , which cannot be modeled with linear algebra, linear algebra is often used as a first-order approximation.
It seems that you're in Germany. We have a dedicated site for Germany. As in the previous edition, the text is well written and gives a thorough discussion of many topics of linear algebra and related fields Overall, I found the book a very useful one It is a suitable choice as a graduate text or as a reference book. The development of the subject is elegant
Steven Roman, Advanced Linear Algebra Having read almost every book mentioned here, I can tell you that "linear algebra done right" by.
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I would suggest starting with a basic level textbook and then put more effort on one or two intermediate level textbooks. Advanced level books may not be a good source for study. This is an erudite and discursive introduction to linear algebra, weighted heavily toward matrices and systems of linear equations. The author has an expansive view of linear algebra, and from time to time draws in some calculus, Fourier series, wavelets, and function spaces, but the approach is always very concrete. But the book also does a good job of moving up and down between various levels of abstraction, according to which level makes the problem at hand easier to comprehend, and geometrical examples and rotations play an important role in the exposition.
A First Course in Linear Algebra is an introductory textbook designed for university sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Along the way, determinants and eigenvalues get fair time.