1.3. Some Classical Combinatorics
2. Basic Matrix Operations
2.2. The Konig Digraph of a Matrix
2.3. Partitioned Matrices
3.1. Matrix Powers and Digraphs
3.3. Permutations with Restrictions
4.1. Definition of the Determinant
4.2. Properties of Determinants
4.3. A Special Determinant Formula
4.4. Classical Definition of the Determinant
4.5. Laplace Determinant Development
5.1. Adjoint and Its Determinant
5.2. Inverse of a Square Matrix
5.3. Graph-Theoretic Interpretation
6. Systems of Linear Equations
6.1. Solutions of Linear Systems
6.3. Solving Linear Systems by Digraphs
6.4. Signal Flow Digraphs of Linear Systems
7.1. Eigenvectors and Eigenvalues
7.2. The Cayley-Hamilton Theorem
7.3. Similar Matrices and the JCF
7.4. Spectrum of Circulants
8.1. Irreducible and Reducible Matrices
8.2. Primitive and Imprimitive Matrices
8.3. The Perron-Frobenius Theorem
9.1. Tensor and Hadamard Product
9.2. Eigenvalue Inclusion Regions
9.3. Permanent and SNS-Matrices
10.1. Electrical Engineering: Flow Graphs
10.2. Physics: Vibration of a Membrane
10.3. Chemistry: Unsaturated Hydrocarbons
