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You are here: Home ▶ Mathematics ▶ Linear Algebra, Infinite Dimensions, and Maple

Linear Algebra, Infinite Dimensions, and Maple

March 24, 2006

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.

Book 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.

Table of 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

Download Free PDF / Read Online

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

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