Linear Algebra Quick Study Guide - FREE chapters on Linear Equations, Determinant, more in the trial


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Boost Your grades with this illustrated quick-study guide. You will use it from college to graduate school and beyond. FREE chapters on Linear Equations, Determinant, more in trial
Last Update:November 29th 2007
User Rating:0.00
License:No key required
Requirements:3MB and Free MobiPocket Reader
ID's:HID: 207116, AAID: 18504

Author's Description

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


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

Table of Contents

I. Linear equations

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

II. 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

III. Matrix decompositions

  • Block LU Decomposition
  • Cholesky decomposition
  • LU decomposition
  • QR decomposition
  • Spectral theorem
  • Singular value decomposition
  • Schur decomposition
    • Schur complement

IV. Computations

  • Transformation Matrix
  • Householder transformation
  • Least squares, linear least squares
  • Gram-Schmidt process

V. Vectors

  • Unit Vector
  • Pseudovector
  • Normal Vector
  • Tangential and Normal Components
  • Scalar multiplication
  • Linear combination
  • Linear span
  • Linear independence
  • Basis

VI. 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

VII. Affine space

  • Affine transformation
  • Affine group


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