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