Elementary linear algebra for advanced spectral problems

Elementary Linear Algebra for Advanced Spectral Problems

The purpose of this article is to discuss a simple linear algebraic tool which has proved itself very useful in the mathematical study of spectral problems arising in elecromagnetism and quantum mechanics. Roughly speaking it amounts to replacing an operator of interest by a suitably chosen invertible system of operators. That approach has a very long tradition and appears constantly under diff...

Problems for Advanced Linear Algebra

• Class will be structured around students presenting complete solutions to the problems in this handout. Please only agree to come to the board when you are confident that you can provide a clear, complete presentation of the solution to the class without looking at your notes. I will not look favorably on instances when you agree to come to the blackboard but are not ready to present. On the ...

Elementary Linear Algebra

A Glossary for Elementary Linear Algebra

NOTE: Text that is wrapped in /* . . . */ refers to facts that you will not understand until after you encounter the listed concept the first time. I want you to keep the glossary and so I make it useful for later back reference and repetition. I don’t use /* . . . */ for material that is only a week ahead. Example: /* some wisdom about eigenvalues */end of M251 Linear Equation: An equation of ...

Notes on Elementary Linear Algebra

C. David Sherrill School of Chemistry and Biochemistry Georgia Institute of Technology Revised August 2005 1 Vectors In quantum mechanics, we are generally interested in complex numbers. Let C denote the set of all n-tuples of complex numbers (a complex n-space). The elements of C may be called “points” or “vectors” in complex n-space. The elements of the complex numbers C are scalars. A vector...