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Linear Algebra Study Guide - FREE chapters on Linear Equations, Determinant, and more in the trial version (Mobi Study Guides) [Kindle Edition]

MobileReference
4.0 out of 5 stars  See all reviews (2 customer reviews)

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Book Description

Boost Your grades with this illustrated study guide. You will use it from college all the way to graduate school and beyond. FREE chapters on Linear equations, Determinant, and more in the trial version.

Features:

- Clear and concise explanations
- Difficult concepts are explained in simple terms
- Illustrated with graphs and diagrams


List of Chapters:
1. Linear equations
2. Matrices
3. Matrix decompositions
4. Computations
5. Vectors
6. Vector spaces
7. Affine space
Table of Mathematical Symbols

Table of Contents:

1. Linear equations

System of linear equations
Determinant
Minor
Cauchy-Binet formula
Cramer's rule
Gaussian elimination
Gauss-Jordan elimination
Strassen algorithm
2. Matrices

Matrix addition
Matrix multiplication
Basis transformation matrix
Characteristic polynomial, Characteristic Equation
Trace
Eigenvalue, eigenvector and eigenspace
Cayley-Hamilton theorem
Spread of a matrix
Symbolic Computation of Matrix Eigenvalues
Jordan normal form
Rank
Matrix inversion,
Pseudoinverse
Adjugate
Transpose
Dot product
Symmetric matrix
Matrix congruence
Congruence relation
Orthogonal matrix
Skew-symmetric matrix
Conjugate transpose
Unitary matrix
Hermitian matrix, Antihermitian
Positive definite: matrix, function, bilinear form
Identity matrix
Pfaffian
Projection
Diagonal matrix, main diagonal
Diagonalizable matrix
Similar matrix
Tridiagonal matrix
Hessenberg matrix
Triangular matrix
Spectral theorem
Stochastic matrix
Toeplitz matrix
Circulant matrix
Hankel matrix
Vandermonde matrix
Block matrix
(0,1)-matrix
Normal Matrix
Sparse matrix
Woodbury matrix identity
Perron-Frobenius theorem
List of Matrices
3. Matrix decompositions

Block LU Decomposition
Cholesky decomposition
LU decomposition
QR decomposition
Spectral theorem
Singular value decomposition
Schur decomposition
Schur complement
4. Computations

Transformation Matrix
Householder transformation
Least squares, linear least squares
Gram-Schmidt process
5. Vectors

Unit Vector
Pseudovector
Normal Vector
Tangential and Normal Components
Scalar multiplication
Linear combination
Linear span
Linear independence
Basis
6. Vector spaces

Basis (Hamel basis)
Dimension theorem for vector spaces (Hamel dimension)
Examples of vector spaces
Linear map
Galilean transformation, Lorentz transformation
Row and Column space
Null space
Rank-nullity theorem
Dual space
Linear function
Linear functional
Orthogonality
Orthogonal complement
Orthogonal projection
Improper rotation
Category of vector spaces
Subspace
Linear Subspace
Normed vector space
Inner product space
7. Affine space

Affine transformation
Affine group

Editorial Reviews

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Product Details

  • File Size: 4909 KB
  • Print Length: 400 pages
  • Publisher: MobileReference (May 11, 2007)
  • Language: English
  • ASIN: B004L9KIJY
  • Text-to-Speech: Enabled
  • X-Ray:
  • Word Wise: Not Enabled
  • Lending: Not Enabled
  • Amazon Best Sellers Rank: #1,099,321 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
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Customer Reviews

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Most Helpful Customer Reviews
3.0 out of 5 stars Unordered but not bad November 5, 2011
Format:Kindle Edition
The book is a pretty good reference book, but cannot really be used for studies since entries come randomly and it's also difficult to search. Content is good, though.
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2 of 3 people found the following review helpful
5.0 out of 5 stars Great reference ebook March 23, 2009
Format:Kindle Edition|Verified Purchase
Linear Algebra Study Guide - FREE chapters on Linear Equations, Determinant, and more in the trial version

After being out of school for quite some time, I needed a book to get me back up to speed on Algebra. This ebook is great. Highly recommended.
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