Linear Algebra
Matrices, Determinants, and Systems of Linear Equations.
Solving systems of linear equations using matrix method.
Elementary transformations. Matrix rank. Solving homogeneous systems of equations.
Gaussian elimination method for solving systems of linear equations.
Symmetric, nonsymmetric, orthogonal, and inverse matrices.
Matrices. Operations with matrices.
Elements of Vector Algebra and Linear Space Theory.
Linear combinations, linear dependence of vectors. Collinear and coplanar vectors.
Basis of a linear space. Decomposition of a vector by basis.
Scalar product of vectors, properties. Length of vectors. Angle between vectors.
Projections of a vector. Direction cosines. Cauchy-Schwarz inequality.
Coordinate transformation. Transition matrix.
Vector and Mixed Product of Vectors.
Eigenvalues and Eigenvectors of Matrices. Methods for Finding Them.
Operations with geometric vectors.
Polar, cylindrical, and spherical coordinate systems. Transition formulas.
