Linear Algebra II

Spectral Theory and Abstract Vector Spaces

Beoordelingen:
( 15 )
208 pages
Taal:
 English
This contains the basic abstract theory of Linear algebra.
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Over de auteur

Kenneth Kuttler received his Ph.D. in mathematics from The University of Texas at Austin in 1981. From there, he went to Michigan Tech. University where he was employed for most of the next 17 years. He joined the faculty of Brigham Young University in 1998 and has been there since this time. Kuttler'...

Description
Content

This contains the basic abstract theory of Linear algebra. It includes a discussion of general fields of scalars, spectral theory, canonical forms, applications to Markov processes, and inner product spaces.

  1. Spectral Theory
    1. Eigenvalues
    2. Some Applications Of Eigenvalues And Eigenvectors
    3. Exercises
    4. Schur’s Theorem
    5. Trace And Determinant
    6. Quadratic Forms
    7. Second Derivative Test
    8. The Estimation Of Eigenvalues
    9. Advanced Theorems
    10. Exercises
  2. Vector Spaces And Fields
    1. Vector Space Axioms
    2. Subspaces And Bases
    3. Lots Of Fields
    4. Exercises
  3. Linear Transformations
    1. Matrix Multiplication As A Linear Transformation
    2. L(V,W) As A Vector Space
    3. The Matrix Of A Linear Transformation
    4. Eigenvalues And Eigenvectors Of Linear Transformations
    5. Exercises
  4. Linear Transformations Canonical Forms
    1. A Theorem Of Sylvester, Direct Sums
    2. Direct Sums, Block Diagonal Matrices
    3. Cyclic Sets
    4. Nilpotent Transformations
    5. The Jordan Canonical Form
    6. Exercises
    7. The Rational Canonical Form
    8. Uniqueness
    9. Exercises
  5. Markov Chains And Migration Processes
    1. Regular Markov Matrices
    2. Migration Matrices
    3. Markov Chains
    4. Exercises
  6. Inner Product Spaces
    1. General Theory 181
    2. The Gram Schmidt Process
    3. Riesz Representation Theorem
    4. The Tensor Product Of Two Vectors
    5. Least Squares
    6. Fredholm Alternative Again
    7. Exercises
    8. The Determinant And Volume
    9. Exercises