1. komponenta

Lecture type	Total
Lectures	30
Exercises	15

* Load is given in academic hour (1 academic hour = 45 minutes)

Matrix algebra. Definition of matrix. Additon of matrix. Scalar multiplication of matrix. Matrix multiplication. Regular matrices. Some special matrices. Application of matrices.
Determinants. Introduction. Determinants of 1st and 2nd order. Definition of permuatation and definition of determinant of random order. Properties. Laplace expansion. Application of determinants in the system of linear equations.
Systems of linear equations. Matrix equation. Solution. Equivalent systems. Elementar transformarions. Matrix rang. Gaussian elimination.
Vector space. Introduction. Linear combination. Linear independance. Basis and dimension. Examples of vector spaces. Application to matrices.
Products. Scalar product. Orthogonality. Examples and applications. Vector product. Definition and application. Mixed product. Application to volume calculation.

Learning outcomes:

Apply matrix calculus.
Solve a system of linear equations.
Calculate eigenvalues and eigenvectors of a linear operator.
Calculate and apply scalar, vector and mixed product.

1. S. Lipschutz, M. Lipson: Schaum's Outline of Linear Algebra. McGraw-Hill, 2001
2. J.Ferguson: Introduction to Linear Algebra in Geology. Springer Verlag, 1994.
3. N.Elezović: Linearna algebra. Element, 1995.

Mandatory course - Regular study - Environmental Sciences