Rating:

( 15 )

154 pages

Language:

English

This contains the basic abstract theory of Linear algebra.

Latest eBooks

About the author

Get ahead at work with our collection of personal development eBooks

Download 1,700+ eBooks on soft skills and professional efficiency, from communicating effectively over Excel and Outlook, to project management and how to deal with difficult people.

- Written by industry-leading experts
- Bite-sized format (1-2hr reading time)
- Easy-to-use and accessible eReader
- Continue reading from where you stopped
- New eBooks added every week

Free 30-day trial
Then $5.99/mo. Cancel at any time.

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.

Click here to download the additional book files using Firefox or any browser which supports mathml.

- Vector Spaces And Fields
- Vector Space Axioms
- Subspaces And Bases
- Lots Of Fields
- Exercises

- Linear Transformations
- Matrix Multiplication As A Linear Transformation
- L (V, W) As A Vector Space
- The Matrix Of A Linear Transformation
- Eigenvalues And Eigenvectors Of Linear Transformations
- Exercises

- Canonical Forms
- A Theorem Of Sylvester, Direct Sums
- Direct Sums, Block Diagonal Matrices
- Cyclic Sets
- Nilpotent Transformations
- The Jordan Canonical Form
- Exercises
- The Rational Canonical Form
- Uniqueness
- Exercises

- Markov Processes
- Regular Markov Matrices
- Migration Matrices
- Absorbing States
- Exercises

- Inner Product Spaces
- General Theory
- The Gram Schmidt Process
- Riesz Representation Theorem
- The Tensor Product Of Two Vectors
- Least Squares
- Fredholm Alternative Again
- Exercises
- The Determinant And Volume
- Exercises

- Self Adjoint Operators
- Simultaneous Diagonalization
- Schur’s Theorem
- Spectral Theory Of Self Adjoint Operators
- Positive And Negative Linear Transformations
- The Square Root
- Fractional Powers
- Square Roots And Polar Decompositions
- An Application To Statistics
- The Singular Value Decomposition
- Approximation In The Frobenius Norm
- Least Squares And Singular Value Decomposition
- The Moore Penrose Inverse
- Exercises

- Index