most recent 30 from http://mathoverflow.net 2013-05-21T07:28:42Z http://mathoverflow.net/feeds/question/50892 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/50892/applied-linear-algebra-textbook dkh 2011-01-02T01:12:04Z 2011-01-02T03:56:23Z

<p>I have a copy of <em>Linear Algebra Done Right</em>, which I worked through years ago in college. I have been using that book to refresh my knowledge, but it does not have an applied or computational aspect to it at all. What would be a good follow-up or companion to <em>Linear Algebra Done Right</em> to introduce me to applied linear algebra, both the theory and practical aspects such as numerical considerations? </p>

http://mathoverflow.net/questions/50892/applied-linear-algebra-textbook/50893#50893 GH 2011-01-02T01:41:46Z 2011-01-02T01:41:46Z

<p>How about Lax's Linear Algebra?</p>

http://mathoverflow.net/questions/50892/applied-linear-algebra-textbook/50894#50894 Jiahao Chen 2011-01-02T01:49:53Z 2011-01-02T02:08:03Z

<p>"Numerical Linear Algebra" by Trefethen and Bau is IMO the single best book to start learning from. It is lucidly written, concise and relatively inexpensive. Perhaps its main drawback is an unconventional presentation starting from singular value decomposition (SVD) and presenting the other standard transformations as derivatives of SVD. It worked for me though.</p> <p>There are many other excellent books out there, but any good book should cover the basics like Gaussian elimination, Cholesky factorization, LU and QR decompositions, Householder reflections and Givens rotations as an absolutely bare minimum. Also essential are applications to solving linear systems, least squares problems and eigenvalue computations. To understand more contemporary algorithms, coverage of Krylov subspace algorithms such as CG and GMRES, as well as sparse matrix algorithms, are considered increasingly important additions to the standard canon above.</p> <p>P.S. The key to numerical work is to figure out methods to solve problems for special matrices (e.g. diagonal matrices or upper triangular matrices), then figure out ways to transform entire classes of matrices into such special forms. This took me a while to appreciate consciously but apparently this is an observation that is too trivial for many textbook authors to write out explicitly. Trefethen and Bau is nice because it actually tries to motivate the development pedagogically rather than presenting a laundry list of Things You Should Know.</p>

http://mathoverflow.net/questions/50892/applied-linear-algebra-textbook/50900#50900 John D. Cook 2011-01-02T03:21:12Z 2011-01-02T03:21:12Z

<p>Golub and Van Loan's book <a href="http://www.amazon.com/gp/product/0801854148?ie=UTF8&amp;tag=theende-20&amp;linkCode=as2&amp;camp=1789&amp;creative=390957&amp;creativeASIN=0801854148" rel="nofollow">Matrix Computations</a> is a classic.</p>

http://mathoverflow.net/questions/50892/applied-linear-algebra-textbook/50901#50901 Dick Palais 2011-01-02T03:56:23Z 2011-01-02T03:56:23Z

<p>Gil Strang's "Linear Algebra and its Applications" is another classic.</p>