The Linear Algebra a Beginning Graduate Student Ought to Know

Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics and which has important applications in all branches of the physical and social sciences and in engineering. However, in recent years the content of linear algebra courses required to complete an undergraduate degree in mathematics -- and even more so in other areas -- at all but the most dedicated universities, has been depleted to the extent that it falls far short of what is in fact needed for graduate study. This is true not only in the areas of theoretical work but also in the areas of computational matrix theory, which are becoming more and more important to the working researcher as personal computers become a common tool. Students are not only less able to formulate or even follow mathematical proofs, they are also less able to understand the underlying mathematics of the numerical algorithms they must use. The resulting knowledge gap has led to frustration and recrimination on the part of both students and faculty alike, with each silently -- and sometimes not so silently -- blaming the other for the resulting state of affairs. This book is written with the in