Basics of Linear Algebra
Description
The course Basics of Linear Algebra is designed to introduce 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 self-study tasks.
Knowledge requirements: completion of the course Welcome to Engee.
Total course time: ~3 hours.
Course program
Matrices. The main types of matrices
The concept of a matrix, the main types of matrices (square, diagonal, identity, triangular, zero matrix, row vector and column vector), the concept of a transposed and Hermitian conjugate matrix are studied.
Basic operations on matrices
Matrix multiplication by a number, addition, subtraction and multiplication of matrices, matrix exponentiation are studied.
Determinants
The concepts of a determinant of the second, third and higher orders, properties of determinants, concepts of minors and cofactors are studied.
The inverse matrix
The concepts of singular and non-singular, adjugate and inverse matrices, and properties of the inverse matrix are studied.
The matrix rank
The concept of the matrix rank, its properties and the calculation of the matrix rank using elementary transformations are studied.
Systems of linear algebraic equations
Systems of linear algebraic equations, solving systems of linear equations using built-in Engee tools, using Kramer formulas, the matrix method and the Gauss method, and studying the consistency of systems of linear equations using the Kronecker-Capelli theorem are studied.
The eigenvalues and eigenvectors of the matrix
The concepts of eigenvalue and eigenvector, their calculation by built-in Engee tools, the use of eigenvalues and eigenvectors to calculate the rating of web pages are studied.