Linear Algebra
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–open source software, fast, simple
–open source software
- online GNU Octave
–proprietary
: good interactive HW exercises, very clear instruction and time-efficient
: Gilbert Strang is good.
and
Systems of Linear Equations: Algebra (pp 1-27)
Systems of Linear Equations: Geometry (pp 29-112)
Linear Transformations and Matrix Algebra (pp 113-185)
Determinants (pp 187-235)
Eigenvalues and Eigenvectors (pp 237-337)
Orthogonality (pp 339-407)
Systems of Equations and Matrices (pp 7-169)
Systems of linear equations
Solving systems using matrices
Using systems of equations
Matrices and matrix operations
Matrix inverses
Elementary matrices
Special forms of square matrices
Determinants
Determinants versus row operations
Determinants, the adjoint, and inverses
Vector Spaces (pp 170-374)
Introduction to vectors
Geometry of vectors
Orthogonal vectors
Geometry of linear systems
Abstract vector spaces
Subspaces
Linear independence
Basis and Coordinates
Dimension
Column, row, and null spaces
Introduction to Matrix Forms (pp 375-413)
Eigenvalues and eigenvectors
Diagonalization
Linear Systems
Solving Linear Systems
Linear Geometry
Reduced Echelon Form
Vector Spaces
Definition of Vector Space
Linear Independence
Basis and Dimension
Maps Between Spaces
Isomorphisms
Homomorphisms
Computing Linear Maps
Matrix Operations
Change of Basis
Projection
Determinants
Definition
Geometry of Determinants
Laplace's Formula
Similarity
Complex Vector Spaces
Similarity
Nilpotence
Jordan Form
Systems of Linear Equations
Vectors
Matrices
Vector Spaces
Determinants
Eigenvalues
Linear Transformations
Representations
Preliminaries
Matrices and Linear Transformations
Determinants
Row Operations
Some Factorizations
Linear Programming
Spectral Theory
Vector Spaces and Fields
Linear Transformations
Linear Transformations Canonical Forms
Markov Chains and Migration Processes
Inner Product Spaces
Self Adjoint Operators
Norms for Finite Dimensional Vector Spaces
Numerical Methods for Finding Eigenvalues
Systems of Linear Equations
Matrix theory
The Determinant
Vectors in Euclidean n-space
Eigenvalues and eigenvectors
Linear transformations
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