Linear Algebra

Matrices, Determinants, and Systems of Linear Equations.

Solving systems of linear equations using matrix method.

Gaussian elimination method for solving systems of linear equations.

Elementary transformations. Matrix rank. Solving homogeneous systems of equations.

Calculation of determinants

Symmetric, nonsymmetric, orthogonal, and inverse matrices.

Matrices. Operations with matrices.

Cramer's Rule.

Elements of Vector Algebra and Linear Space Theory.

Linear combinations, linear dependence of vectors. Collinear and coplanar vectors.

Coordinate transformation. Transition matrix.

Basis of a linear space. Decomposition of a vector by basis.

Projections of a vector. Direction cosines. Cauchy-Schwarz inequality.

Polar, cylindrical, and spherical coordinate systems. Transition formulas.

Scalar product of vectors, properties. Length of vectors. Angle between vectors.

Eigenvalues and Eigenvectors of Matrices. Methods for Finding Them.

Vector and Mixed Product of Vectors.

Double vector product

Operations with geometric vectors.