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.

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

Coordinate transformation. Transition matrix.

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

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

Eigenvalues and Eigenvectors of Matrices. Methods for Finding Them.

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

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

Double vector product

Operations with geometric vectors.

Vector and Mixed Product of Vectors.