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Linear Algebra Quick Study Guide - FREE chapters on Linear Equations, Determinant, more in the trial -
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.
Features
- 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,
- Adjugate
- Transpose
- Dot product
- Symmetric matrix
- Matrix congruence
- 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
- Similar matrix
- Tridiagonal matrix
- Hessenberg matrix
- Triangular matrix
- Spectral theorem
- Stochastic matrix
- Toeplitz 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
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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