Linear Algebra
Matrices, Determinants, and Systems of Linear Equations.
Solving systems of linear equations using matrix method.
Symmetric, nonsymmetric, orthogonal, and inverse matrices.
Gaussian elimination method for solving systems of linear equations.
Elementary transformations. Matrix rank. Solving homogeneous systems of equations.
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.
Eigenvalues and Eigenvectors of Matrices. Methods for Finding Them.
Vector and Mixed Product of Vectors.
Polar, cylindrical, and spherical coordinate systems. Transition formulas.