Linear Algebra Quick Study Guide (Palm OS) - Boost Your grades with this illustrated quick-study guide. You will use it from college to graduate school and beyond. Intended for everyone interested in Math and Science, particularly undergraduate and graduate students.
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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· Difficult concepts are explained in simple terms
· Illustrated with graphs and diagrams
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· 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.
· FREE chapters on Linear Equations, Determinant, and more in the trial version.
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