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Key definitions, theorems and formulas (part 1 of 2)
TItle
To the Student
Systems of Linear Equations and Matrices
Systems of Linear Equations: Matrix Methods
Linear Systems without Unique Solutions
Matrix Arithmetic
Matrix Algebra
Matrix Inversion
Partitioned Matrices: Numerical Considerations
Extended Application: Networks and Graphs
Summary
Determinants
The Determinant Function and Cramer's Rule
Laplace Expansion of Determinants
Properties of Determinants
Determinants and Matrix Inversion
Summary
Vector Spaces
Examples and Definition of a Vector Space
Linear Dependence and Independence
Spanning Set: Subspace
Ordered Basis and Dimension
Matrices: Row and Column Spaces
Summary
Inner Product Spaces
Distance and Angle in R^2 and R^3
Cross Products in R^3 (optional)
Real Inner Products
Geometry in Real Inner-Product Spaces
The Gram-Schmidt Process
Complex Vectors, Matrices, Inner Products
Extended Application: Least Squares Fit
Summary
Linear Transformations
Definitions and Examples
The Range and Kernel of a Linear Transformation
Matrix Representations
The Algebra of Linear Transformations
Change of Basis and Similarity
Orthogonal Linear Transformations
Summary
Eigenvalues, Eigenvectors, and Some Applications
Eigenvalues and Eigenvectors
Similarity to a Diagonal Matrix
Real Symmetric Matrices
Quadratic Forms, Conics, and Quadric Surfaces
Extended Application: Markov Chains
Complex Eigenvalues
Extended Application: Systems of Differential Equations
Summary
Appendices
The Complex Numbers
Sets and Functions
Algorithms
References
The Greek Alphabet and Frequently Used Symbols
Answers and Solutions to Selected ExercisesIndex
Key definitions, theorems and formulas (part 2 of 2)