Linear Algebra, Infinite Dimensions, and Maple

Linear Algebra, Infinite Dimensions, and Maple can be downloaded free of charge in pdf format. These notes evolved in the process of teaching a beginning graduate course in Hilbert Spaces.

Description

The first edition was simply personal, handwritten notes prepared for lecture. A copy was typed and given to the students, for it seemed appropriate that they should have a statement of theorems, examples, and assignments. With each teaching of the course, the notes grew.

Contents

  • A Decomposition for Matrices
  • Exp(tA)
  • Self Adjoint Transformations in Inner-Product Spaces
  • The Gerschgorin Circle Theorem
  • Convergence
  • Orthogonality and Closest Point Projection
  • Orthogonal, Nonexpansive, & Self-Adjoint Projections
  • Orthonormal Vectors
  • The Finite Dimensional Paradigm
  • Bounded Linear Maps from E to C
  • Applications to Differential Equations
  • The Simple Paradigm from E to E
  • Adjoint Operators
  • Compact Sets
  • Compact Operators
  • The Space of Bounded Linear Operators
  • The Eigenvalue Problem
  • Normal Operators and The More General Paradigm
  • Compact Operators and Orthonormal Families
  • A Characterization of Compact Operators
  • The Fredholm Alternative Theorems
  • Closed Operators
  • The Deficiency of A
  • A Problem in Control
  • Approximation in a Hilbert Space with a reproducing kernel

Book Details

Author(s): James V. Herod
Format(s): PDF
Link: Download.







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