The Linear Algebra a Beginning Graduate Student Ought to Know

• Main Author: Golan, Jonathan S. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Dordrecht : Springer Netherlands, 2007.
• Subjects: Mathematics.; Numerical analysis.; Algebra.; Associative rings.; Rings (Algebra).; Matrix theory.; Nonassociative rings.; Algorithms.; Linear and Multilinear Algebras, Matrix Theory.; Associative Rings and Algebras.; Non-associative Rings and Algebras.; Numeric Computing.

Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as computer science, the physical and social sciences, and engineering. It entails an extensive corpus of theoretical results as well as a large body of...

Table of Contents:

• Notation and terminology
• Fields
• Vector spaces over a field
• Algebras over a field
• Linear independence and dimension
• Linear transformations
• The endomorphism algebra of a vector space
• Representation of linear transformations by matrices
• The algebra of square matrices
• Systems of linear equations
• Determinants
• Eigenvalues and eigenvectors
• Krylov subspaces
• The dual space
• Inner product spaces
• Orthogonality
• Selfadjoint Endomorphisms
• Unitary and Normal endomorphisms
• Moore-Penrose pseudoinverses
• Bilinear transformations and forms.