Línuleg algebra með tölvunarfræði

Námsgrein	T-201-LINC
Önn	20241
Einingar	6
Skylda	Nei

Ár	1. ár
Önn	Vorönn/Spring 2024
Stig námskeiðs	Óskilgreint
Tegund námskeiðs	Valnámskeið
Undanfarar	T-103-STST, Strjál stærðfræði fyrir verkfræðinema T-111-PROG, Forritun T-117-STR1, Strjál stærðfræði I
Skipulag	TD-Staðarnám - 12 vikna
Kennari	Christoph Lohrmann
Lýsing
A big portion (?) of modern technology is based on concepts from linear algebra, that are also essential in many areas of computer science, such as graphics, image processing, cryptography, machine learning, computer vision, optimization, graph algorithms, quantum computation, computational biology, bioinformatics, information retrieval and web search. Two basic elements of linear algebra are vectors and matrices. This course teaches the basics of vectors, matrices and algorithms based on them. The student will learn concepts and methods, how to work with them in Python as well as think about and solve various problems in computer science with linear algebra.
Námsmarkmið
Knowledge • Understand the basic concepts of linear algebra related to matrices, vectors and vector spaces. • Understand the terms linear combination, span and generating set. • Know what a basis is. • Know what similar matrices are. • Know what a diagonalizable matrix is. • Know what linearly dependent vectors are. • Understand the relationship between a diagonalizable matrix and linearly independent eigenvectors. • Understand orthogonal projections in many dimensions and orthogonalization. • Understand linear projections. • Understand the terms eigenvalue and eigenvector. • Know what QR factorization is. • Be familiar with linear algebra operations in Python. Skills • Can multiply vector and matrix, matrix and vector and two matrices. • Be able to determine whether vectors are linearly dependent. • Can find a generating set. • Can change a base. • Can solve linear equations with Gaussian elimination. • Can find the null set of an array and the solution set of a linear equation. • Can find the inverse of an invertible matrix. • Can use orthogonalization to find to find closest point and to solve other problems. • Can use the power method. • Can work with vectors and matrices in Python • Can solve problems with Python. • Be able to create programs in Python to implement matrix and vector algorithms, apply them to real data to solve various tasks such as analyzing and blurring faces and error-correcting code. Competences • Have the knowledge to look for the application of linear algebra in computer science. Have the knowledge to program solutions to linear algebra problems. • Have the knowledge to apply ´best approximation´ to solve various problems, e.g. image compression, least squares method, principal component analysis and information retrieval.
Námsmat
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Lesefni
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Tungumál	Enska