Linear Algebra

Aim

To give a unified framework for geometrical and algebraic techniques, with applications in analysis, mechanics, computer graphics, numerical analysis, mathematical statistics, control theory, linear optimization and other subjects. It is also included to develop the ability of using the mathematical language both written and oral. It is necessary for the participant to be able to

solve systems of linear equations

work with inner and cross product

calculate with matrices and determinants

calculate with vectors and coordinates in a vector space

determine the matrix for a linear transformation and the kernel and the range for such matrices

determine ON-basis in an inner product space

do orthogonal projection on subspaces and to use least squares approximations

solve problems by changing basis

determine and to use eigenvalues and eigenvectors in different problems

use the spectral theorem in different problems

determine the canonical basis of quadratic forms and to use these to solve geometrical problems.

carry out inspections of results and partial results, in order to verify that these are correct or reasonable

solve system of linear ordinary differential equations Course content Vectors, straight lines and planes. Linear systems of equations. Matrices and determinants. Vector spaces. Euclidean spaces.Linear mappings. Isometric and symmetric mappings. Eigenvalues and eigenvectors. Diagonalization. Otrhogonality. Quadratic forms. Distance and approximation. System of linear ordinary differential equations Teaching and working methods The course is given in the form of lectures and tutorials. Examination TEN1Written examination6 creditsU, 3, 4, 5KTR3Individual assignment0 creditsU, GKTR4Individual assignment0 creditsU, GGrades for examination modules are decided in accordance with the assessment criteria presented at the start of the course. Grades Four-grade scale, LiU, U, 3, 4, 5 Other information About teaching and examination languageThe teaching language is presented in the Overview tab for each course. The examination language relates to the teaching language as follows: If teaching language is “Swedish”, the course as a whole could be given in Swedish, or partly in English. Examination language is Swedish, but parts of the examination can be in English.If teaching language is “English”, the course as a whole is taught in English. Examination language is English.If teaching language is “Swedish/English”, the course as a whole will be taught in English if students without prior knowledge of the Swedish language participate. Examination language is Swedish or English depending on teaching language.OtherThe course is conducted in such a way that there are equal opportunities with regard to sex, transgender identity or expression, ethnicity, religion or other belief, disability, sexual orientation and age.The planning and implementation of a course should correspond to the course syllabus. The course evaluation should therefore be conducted with the course syllabus as a starting point. The course is campus-based at the location specified for the course, unless otherwise stated under “Teaching and working methods”. Please note, in a campus-based course occasional remote sessions could be included. Department Institutionen för teknik och naturvetenskap Course literature CompendiaKompendium utgivet vid ITN.

Content

Vectors, straight lines and planes. Linear systems of equations. Matrices and determinants. Vector spaces. Euclidean spaces.Linear mappings. Isometric and symmetric mappings. Eigenvalues and eigenvectors. Diagonalization. Otrhogonality. Quadratic forms. Distance and approximation. System of linear ordinary differential equations