Document Type
Working Paper
Publication Date
7-23-2015
Abstract
Table of Contents:
1. Systems of Linear Equations and Matrices
- Systems of Linear Equations
- Elementary Row Operations
- Row Reduction and Reduced Row-Echelon Form
- Solutions of Systems of Linear Equations
- Matrix Operations
- Matrix Inverses
2. Euclidean 2-Space and 3-Space
- Vectors in the Plane and in Space
- The Dot Product
- Cross Product
- Lines in Space
- Planes in Space
3. Determinants
- The Definition of Determinant
- Elementary Row Operations and the Determinant
- Elementary Matrices and the Determinant
- Applications of the Determinant
4. Vector Spaces and Subspaces
- Vector Spaces
- Subspaces
- Linear Dependence and Independence
- Basis and Dimension
5. Linear Transformations
- Definition of Linear Transformation
- The Kernel and Range of a Linear Transformation
- Isomorphisms and Coordinate Vectors
- Similarity
6. Eigenvalues and Eigenvectors
- Eigenvalues, Eigenvectors, and Eigenspaces
- The Characteristic Polynomial
- Diagonalization
- Eigenvalues and Linear Operators
7. (Real) Inner Product Spaces
- Introduction
- Angle and Orthogonality
- Orthogonal and Orthonormal Bases
- Gram-Schmidt
- Least Squares
- Inner Product Space Isomorphisms and Orthogonal Matrices
- Symmetric Matrices and Orthogonal Diagonalizability
8. Applications
- Quadratic Forms
- Constrained Optimization of Quadratic Forms
- Conic Sections
- Quadric Surfaces
- Positive Definite Matrices
- Singluar Value Decomposition
- Matrix Norms
- The Pseudoinverse
Selected Answers
Index
Recommended Citation
Scully, Daniel, "Linear Algebra" (2015). Math Faculty Publications. 1.
https://repository.stcloudstate.edu/mathstat_facpubs/1
