Linear Algebra Study Guide [NOOK Book]

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Overview

Boost Your grades with this illustrated Study Guide. You will use it from college all the way to graduate school and beyond.

Features

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

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 multiplication
• Basis transformation matrix
• Characteristic polynomial, Characteristic Equation
• Trace
• Eigenvalue, eigenvector and eigenspace
• Cayley-Hamilton theorem
• Symbolic Computation of Matrix Eigenvalues
• Jordan normal form
• Rank
• Matrix inversion,
• Pseudoinverse
• 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

...

Product Details

• ISBN-13: 9781605010823
• Publisher: MobileReference
• Publication date: 1/1/2010
• Series: Mobi Study Guides
• Sold by: Barnes & Noble
• Format: eBook
• Sales rank: 882,538
• File size: 6 MB

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