Linear algebra

Description

The subject provides students with the formation of theoretical knowledge and analytical skills on the fundamental concepts and methods of linear algebra. matrices and operations on them, calculation of determinants and their main properties, vectors, vector spaces and linear spaces are studied within the subject. systems of linear algebraic equations, the existence of their solution and various solution methods, as well as the basic principles of linear transformations are reviewed. the concepts of eigennumber and eigenvector, polynomials and their solution methods, quadratic forms and their canonicalization are investigated. also, basic numerical methods and decomposition approaches used in solving linear algebra problems are studied. the subject is aimed at developing students' ability to formally express mathematical problems, choose a suitable solution method, build solution algorithms and evaluate their efficiency.

Course learning outcomes

1. 1

   CLO 1: He should know the general definition of a matrix, its different types, all operations on matrices, the main properties of these operations and matrix transposition. methods of calculating two- and three-order determinates should be mastered.

2. 2

   CLO 2: Must have knowledge such as the concept of minor and algebraic complement, the formula for dividing the determinant by row or column, the inductive definition of the higher order determinant, and also methods of calculation. must be able to calculate the determinant of the product of two matrices and calculate the inverse of a square matrix. must be able to perform operations on orthogonal matrices and block matrices.

3. 3

   CLO 3: He should know the concept of n-dimensional vector, the definition of linear dependence of a system of vectors, the necessary and sufficient condition of linear dependence, and the methods of calculating the rank of a matrix. must have knowledge of definition of linear space, basis, dimension, linear transformation, matrix of linear transformation and operations on linear transformations. the concepts of eigenvalue and vector of matrix, algorithm of finding eigenvalue and appropriate eigenvector should be mastered.

4. 4

   CLO 4: He should have knowledge about the system of linear algebraic equations, the system of homogeneous and non-homogeneous linear algebraic equations, the system of convergent and non-convergent linear algebraic equations. he should know how to solve a system of linear algebraic equations by the cramer and gauss method and how to solve a system of homogeneous linear algebraic equations.

5. 5

   CLO 5: Must have knowledge of polynomials, arithmetic operations on them, residual division of polynomials, bezou's theorem, and horner's scheme algorithm. lagrange for finding the limits of the real roots of a polynomial. must know newton's methods.

6. 6

   CLO 6: He should know the quadratic form, the matrix representation of the quadratic form, and the quadratic form in the canonical form. must be able to work with lagrangian and jacobian methods to bring quadratic form to canonical form.