Linear Algebra 2400-PP1ALa
1 Systems of linear equations: solutions and general solutions, matrices, elementary matrix operations, solving the system of equations using Gaussian elimination.
2 Linear (or vector) spaces: examples, linear subspaces, linear combinations of vectors, linear independence, basis and dimension of a linear space, the coordinates of the vector in a given basis.
3 Linear transformations: examples , matrix representation of linear transformations, the algebra of linear transformations and matrix operations, matrix algebra .
4 Determinants: properties of determinants and methods of calculation.
5 Matrix Inverse and methods of finding the inverse matrix.
6 Applications determinant and rank of a matrix to solve linear equations : Kronecker - Capelli theorem and Cramer.
7 Vectors and eigenvalues of linear transformations: Find the eigenvalues, the characteristic polynomial, bases of eigenspaces and diagonalisation of matrices.
8 Applications matrix diagonalisation.
9 Affine subspaces (or layers) of linear spaces, equations of the line and plane.
10 The standard scalar product: vector length, magnitude of vectors, orthogonal bases and orthonormal bases and the Gram-Schmidt procedure.
11 Quadratic forms: examples of matrix quadratic forms, Sylvester criterion of positive definiteness and tests of semidefinitness using eigenvalves.
Type of course
The ability to understand and use linear algebra in statistics, econometrics and mathematical models of decision making. Basic techniques of linear algebra, including: solving systems of linear equations, finding bases and dimensions of space, calculating rows, determinants and matrix inverse, finding the eigenvectors of linear transformations, diagonalization, testing positive (negative) definiteness of quadratic forms.
Evaluation of the course is via a written examination.
Linear Algebra, K.M. Hoffman and R. Kunze, Pearson; 2 edition (April 25, 1971)
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
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