Linear Algebra

Matrices, Determinants, and Systems of Linear Equations.

Solving systems of linear equations using matrix method.

Symmetric, nonsymmetric, orthogonal, and inverse matrices.

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

Matrices. Operations with matrices.

Gaussian elimination method for solving systems of linear equations.

Calculation of determinants

Cramer's Rule.

Elements of Vector Algebra and Linear Space Theory.

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

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

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

Coordinate transformation. Transition matrix.

Eigenvalues and Eigenvectors of Matrices. Methods for Finding Them.

Double vector product

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

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

Operations with geometric vectors.

Vector and Mixed Product of Vectors.