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LINEAR ALGEBRA STUDY GUIDE

Boost Your grades with this illustrated 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.


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Audience:

Intended for everyone interested in Math and Science, particularly undergraduate and graduate students.

Features:

  • Clear and concise explanations
  • Difficult concepts are explained in simple terms
  • Illustrated with graphs and diagrams
  • Search for the words or phrases
  • Access the guide anytime, anywhere - at home, on the train, in the subway.
  • Use your down time to prepare for an exam.
  • Always have the guide available for a quick reference.
  • Automatic synchronization between the handheld and the desktop PC. You could read half of the book on the handheld, then finish reading on the desktop. Annotations and drawings are also synchronized.

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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