Course "Fundamentals of Linear Algebra"
Description
The Linear Algebra course is designed to introduce the basic concepts of linear algebra such as matrices, determinants, systems of linear algebraic equations, eigenvalues and eigenvectors.
Each section of the course contains brief theoretical information, practical examples and assignments for self-completion.
Knowledge Requirements: Completion of the course Welcome to Engee course.
Total course time: ~3 hours.
Course Programme
Matrices. Basic types of matrices.
The concept of matrix, the main types of matrices (square, diagonal, unit, triangular, zero matrix, vector-row and vector-column), the concept of transposed and Hermite-conjugate matrix are studied.
Basic operations on matrices.
Multiplication of a matrix by a number, addition, subtraction and multiplication of matrices, raising a matrix to a degree are studied.
Determinants.
The concepts of determinant of second, third and higher orders, properties of determinants, concepts of minors and algebraic complements are studied.
Inverse matrix.
The concepts of degenerate and nondegenerate, adjoint and inverse matrix, properties of inverse matrix are studied.
The rank of a matrix.
The concept of matrix rank, its properties and calculation of matrix rank with the help of elementary transformations are studied.
Systems of linear algebraic equations.
We study systems of linear algebraic equations, the solution of systems of linear equations by the built-in means of Engee, by Cramer’s formulae, by the matrix method and Gauss method, the study of the jointness of systems of linear equations using the Kronecker-Capelli theorem.
Eigenvalues and eigenvectors of a matrix.
The concepts of eigenvalues and eigenvectors, their calculation by the built-in Engee tools, application of eigenvalues and eigenvectors to calculate the rating of web pages are studied.