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1. Vectors and matrices

1.1. Definitions and terminology
1.2. Hungarian method (optional section)
1.3. Operations on matrices
1.4. Linear system of equations
1.5. Computation of an inverse matrix
1.6. LU decomposition
1.7. QR decomposition
1.8. Cholesky decomposition

2. Vector space

2.1. Definitions and examples
2.2. Subspace
2.3. Dimension, basis
2.4. Change of basis
2.5. Linear mappings

3. The rank of a matrix, determinant

3.1. Definitions and terminology
3.2. The rank of a matrix: computation
3.3. Some applications
3.4. The determinant of a matrix
3.5. Applications of determinant: curves and surfaces

4. Eigenvalues and -vectors of a matrix

4.1. Definitions and terminology
4.2. Diagonalizable matrices
4.3. An application: linear systems of differential equations
4.4. Discrete linear (digital) systems and matrices
4.5. Dynamic systems (optional section, under construction)
4.6. Location of eigenvalues
4.7. Numerical computation of eigenvalues

5. On solving linear systems of equations

5.1 Norm and convergence, state-transition matrix e^At
5.2. Iteration methods of the form ^{(k + 1)} = G^(k) +
5.3. The Jacobi method
5.4. The Gauss - Seidel method
5.5. Over determined system, the least squares method
5.6. The projection method
5.7. Condition number

6. Polynomials and functions of matrices