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Linear Algebra II

Spectral Theory and Abstract Vector Spaces

Linear Algebra II
3,9 (15 Opiniones)
ISBN: 978-87-403-0241-7
1 edición
Páginas : 208
  • Price: 129,00 kr
  • Price: €13,99
  • Price: £13,99
  • Price: ₹250
  • Price: $13,99
  • Price: 129,00 kr
  • Price: 129,00 kr

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Acerca del libro

  1. Descripción
  2. Contenido

Descripción

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.

Contenido

  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
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